The proof of mass vector.
Ka-In Yen
Ka-In Yen
yen...@yahoo.com.tw
http://www.geocities.com/redlorikee
Introduction:
In this paper, we will prove that linear mass density and
surface mass density are vector, and the application of mass
vector is presented.
1. The unit of vector.
In physics, The unit of three-dimensional cartesian coordinate
systems is meter. In this paper, a point of 3-D coordinate
system is written as
(p1,p2,p3) m, or (p:3) m
and a vector is written as
<a,b,c> m, or <a:3> m
or
l m<i,j,k> = <a,b,c> m
where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
and <i,j,k> is a unit vector which gives the direction of
the vector.
For three reasons, a magnitude of a vector can not add to a
scalar:
i) The magnitude belongs to the set of vector; it's a
portion of a vector. Scalar belongs to a field.
ii) The magnitude is real non-negative number, but scalar
is real number.
iii) The unit of magnitude is meter, but scalar has no unit.
This is a major difference between physics and mathematics.
5m+3 is meaningless.
2. Linear mass density is a vector.
The mass of a string is M kg, and the length of the string
is l m<i:3>. Where l m is the magnitude of the length, and
<i:3> is a 3-D unit vector which gives the direction of the
string. Then the linear mass density of the string is:
M/(l<i:3>)=(M/l) (kg/m)<i:3>
The direction, <i:3>, is not changed by "division", so we
can move <i:3> from denominator to numerator. A direction
is changed by -1 only. A proof is found in Clifford algebras:
[Proof]
k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
=(k/l) <i,j,k>
where l is the magnitude of <a,b,c>, and <i,j,k> is the
unit vector of <a,b,c>.
[Proof]
3. Surface mass density is a vector.
A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
and <j:3> are unit vectors. The area vector of the parallelogram
is the cross product of these two vectors.
l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
= lh abs(sin(theta)) (m^2)<k:3>
Where theta is the angle between <i:3> and <j:3>. <k:3> is
a unit vector which is perpendicular to <i:3> and <j:3>.
For AXB=-BXA, an area has two directions.
We can divide the area vector by the length vector.
lh*abs(sin(theta))<k:3>/[l<i:3>]
=h<i:3>X<j:3>/<i:3>
=h(<i:3>X<j:3>)X<i:3>
(The direction, <i:3>, is not changed by "division", and
the division is replaced by a cross product.)
=-h<i:3>X(<i:3>X<j:3>)
=-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
(where o is dot product.)
=-h(cos(theta)<i:3>-<j:3>)
=h(<j:3>-cos(theta)<i:3>) m
The result is a rectangle, not the original parallelogram. We
can test the result.
h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>
The magnitude of the area vector is conserved, but the direction
is opposite.
The mass of a round plate is M kg, and the area vector is
A m^2<i:3>; then the surface mass density is
M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>
4. Mass vector in physics.
Mass vector has been found in two equations: 1) the velocity
equation of string. 2) Bernoulli's equation.
i) For waves on a string, we have the velocity equation:
v=sqrt(tau/mu). v is velocity of wave, tau is tension
applying to string, and mu is linear mass density of
string. We can rewrite the equation:
mu=tau/v^2.
In the above equation, the mu is parallel to tau, and both
of them are vector.
ii) Bernoulli's equation is:
P + k*v^2/2=C (P is pressure, k is volume density, and v is
velocity. Here we neglect the gravitational term.)
Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
equation(where <i:3> is a unit vector),
P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
F<i:3> + L<i:3>*v^2/2=C*A<i:3>
(where F is the magnitude of force, and L is the magnitude
of linear mass density.)
These two equations are well used in the theory "Magnetic force:
Combining Drag force and Bernoulli force of ether dynamics."
For detail, please refer to my site:
http://www.geocities.com/redlorikee
Eric Gisse
Ka-In Yen wrote:
> The proof of mass vector.
>
> Ka-In Yen
> yen...@yahoo.com.tw
> http://www.geocities.com/redlorikee
Geocities's place as a shithole continues to be secured by those who
inhabit it.
>
>
> Introduction:
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
>
> 1. The unit of vector.
>
> In physics, The unit of three-dimensional cartesian coordinate
> systems is meter. In this paper, a point of 3-D coordinate
> system is written as
>
> (p1,p2,p3) m, or (p:3) m
>
> and a vector is written as
>
> <a,b,c> m, or <a:3> m
Your terminology will confuse those who are actually educated because
<a,b,c> is actually the triple scalar product of a,b,c multiplied by a
scalar quantity "m".
>
> or
>
> l m<i,j,k> = <a,b,c> m
>
> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> and <i,j,k> is a unit vector which gives the direction of
> the vector.
Taking the absolute value of a manifestly positive object is pointless.
Your nonstandard way of expressing vectors should be corrected.
>
> For three reasons, a magnitude of a vector can not add to a
> scalar:
> i) The magnitude belongs to the set of vector; it's a
> portion of a vector. Scalar belongs to a field.
> ii) The magnitude is real non-negative number, but scalar
> is real number.
> iii) The unit of magnitude is meter, but scalar has no unit.
> This is a major difference between physics and mathematics.
> 5m+3 is meaningless.
Physics uses it correctly. The difference is in your imagination.
[snip - LENGTH IS NOT A VECTOR]
>
> 4. Mass vector in physics.
>
> Mass vector has been found in two equations: 1) the velocity
> equation of string. 2) Bernoulli's equation.
It was explained to you last time that you are mistaken.
>
> i) For waves on a string, we have the velocity equation:
>
> v=sqrt(tau/mu). v is velocity of wave, tau is tension
> applying to string, and mu is linear mass density of
> string. We can rewrite the equation:
>
> mu=tau/v^2.
>
> In the above equation, the mu is parallel to tau, and both
> of them are vector.
Whats the square root of a vector?
Your misconceptions were pointed out to you the last time you mentioned
your "examples".
>
> ii) Bernoulli's equation is:
>
> P + k*v^2/2=C (P is pressure, k is volume density, and v is
> velocity. Here we neglect the gravitational term.)
These are all scalar quantities.
>
> Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
> equation(where <i:3> is a unit vector),
>
> P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
> F<i:3> + L<i:3>*v^2/2=C*A<i:3>
> (where F is the magnitude of force, and L is the magnitude
> of linear mass density.)
>
> These two equations are well used in the theory "Magnetic force:
> Combining Drag force and Bernoulli force of ether dynamics."
> For detail, please refer to my site:
> http://www.geocities.com/redlorikee
There is zero useful content on your site.
PD
I've already explained to you, KY, that your mathematical steps 1 by 1
are ok. The physical meaning that you associate with those steps is
what is faulty.
PD
dedanoe
libra is functional as long as it keeps equal force/mass ratio for
every weight it measures. From Archimedes we have:
Force_1/Force_2=Mass_1/Mass_2=Distance_2/Distance_1. It's been a long
time from the moment when I discarded mass. I do physics only with
forces, distances and phases of oscillations.
www.geocities.com/dedanoe
http://dedanoe.tripod.com/index.html
Ka-In Yen
Dear Eric,
Thank you for your comment. I will correct it. The above notation
will be used in this thread only.
>
> >
> > For three reasons, a magnitude of a vector can not add to a
> > scalar:
> > i) The magnitude belongs to the set of vector; it's a
> > portion of a vector. Scalar belongs to a field.
> > ii) The magnitude is real non-negative number, but scalar
> > is real number.
> > iii) The unit of magnitude is meter, but scalar has no unit.
> > This is a major difference between physics and mathematics.
> > 5m+3 is meaningless.
>
> Physics uses it correctly. The difference is in your imagination.
>
> [snip - LENGTH IS NOT A VECTOR]
>
The equation of magnetic force:
F=iLXB
L is a length vector. Please refer to
http://www.physics.wsu.edu/academics/labs/102Labs/Current_Balance(8-12-02).htm
> >
> > 4. Mass vector in physics.
> >
> > Mass vector has been found in two equations: 1) the velocity
> > equation of string. 2) Bernoulli's equation.
>
> It was explained to you last time that you are mistaken.
>
> >
> > i) For waves on a string, we have the velocity equation:
> >
> > v=sqrt(tau/mu). v is velocity of wave, tau is tension
> > applying to string, and mu is linear mass density of
> > string. We can rewrite the equation:
> >
> > mu=tau/v^2.
> >
> > In the above equation, the mu is parallel to tau, and both
> > of them are vector.
>
> Whats the square root of a vector?
>
Good question!!!
An area vector is A m^2<i:3>. <i:3> is a unit vector.
What's the result of sqrt( A m^2<i:3> )? Or what's a
square giving the area vector A m^2<i:3>?
We can find a pair of vectors of a square: l m<j:3> and
l m<k:3>. <j:3> and <k:3> are unit vector. These two
vectors meet:
i) l^2=A.
ii) <j:3>X<k:3>=<i:3>. These three vectors are perpendicular
to each other.
In fact, we can find infinite pairs of vectors on a plane which
meet i) and ii).
Ka-In Yen
Magnetic force: Drag and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Ka-In Yen
Dear PD,
Thank you for your comment. The vector of linear density and surface
density have been used for a long time.
Current density(J) is a surface density and a vector; its unit is
A/m^2.
Electric field(E) is linear density and a vector; Its unit is V/m.
Displacement(D) is surface density and a vector; Its unit is coul/m^2.
Reference: Classical Electrodynamics(J.D. Jackson) p.820
Ka-In Yen
Magnetic force: Drag and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
PD
First of all, I find it interesting that you define anything that has a
power of length in the denominator as a density. That's not completely
unreasonable.
But to assume that because *one* quantity has density-like units and is
a vector does not mean that *all* quantities that have comparable units
are also vectors.
I'll give you an example of this. Torque and energy have identical
units: N-m. However, one is explicity defined as a scalar quantity and
the other is explicity defined as a vector quantity. No comparison of
the units can gloss over the fact that the two quantities are
inherently different in nature. They *behave* differently under
coordinate transformations.
PD
Ka-In Yen
PD wrote:
> Ka-In Yen wrote:
Dear PD,
Thank you for your question. I suggest different notations
for them: N X m (X is cross product) for torque and Nm for energy.
Ka-In Yen
Magnetic force: Drag force and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
PD
An interesting suggestion but not generally required. There is also the
subtlety when one is referring to a vector quantity or the (scalar)
magnitude of the same vector quantity, as you've noticed.
PD
Lynx Xiong
why wont you eat your sandwitch first
Ka-In Yen
Ka-In Yen wrote:
> The proof of mass vector.
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
> 3. Surface mass density is a vector.
> A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
> and <j:3> are unit vectors. The area vector of the parallelogram
> is the cross product of these two vectors.
> l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
> = lh abs(sin(theta)) (m^2)<k:3>
> Where theta is the angle between <i:3> and <j:3>. <k:3> is
> a unit vector which is perpendicular to <i:3> and <j:3>.
> For AXB=-BXA, an area has two directions.
...
> We can divide the area vector by the length vector.
> lh*abs(sin(theta))<k:3>/[l<i:3>]
> =h<i:3>X<j:3>/<i:3>
> =h(<i:3>X<j:3>)X<i:3>
> (The direction, <i:3>, is not changed by "division", and
> the division is replaced by a cross product.)
> =-h<i:3>X(<i:3>X<j:3>)
> =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
> (where o is dot product.)
> =-h(cos(theta)<i:3>-<j:3>)
> =h(<j:3>-cos(theta)<i:3>) m
> The result is a rectangle, not the original parallelogram. We
> can test the result.
> h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>
> The magnitude of the area vector is conserved, but the direction
> is opposite.
The equation of magnetic force is "vector division by vector".
F=iLXB (X is corss product).
L is a length vector; assuming L=l m<i:3>, <i:3> is a unit vector.
B is magnetic flux density. Its unit is tesla, or Wb/m^2. Wb, Weber,
is the unit of magnetic flux. Assuming
B= b (Wb/m^2)<j:3>, <j:3> is a unit vector.
Since B is a vector of surface density, we can rewrite it:
B= b Wb/(m^2<j:3>), <j:3> is moved to denominator.
LXB= l m<i:3> X b (Wb/m^2)<j:3>
= l m<i:3> * b Wb /(m^2<j:3>)
= lb Wb m<i:3>/(m^2<j:3>)
It's VDV.
Ka-In Yen
Magnetic force: Drag and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Ka-In Yen
Vector algebra was abused by physicists for hundred years.
A GREAT DISASTER!!!
Ka-In Yen
Magnetic force: Drag nd Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Ka-In Yen wrote:
> The proof of mass vector.
>
Ka-In Yen
> Ka-In Yen wrote:
> > The proof of mass vector.
> > In this paper, we will prove that linear mass density and
> > surface mass density are vector, and the application of mass
> > vector is presented.
> >
> >
> > P + k*v^2/2=C (P is pressure, k is volume density, and v is
> > velocity. Here we neglect the gravitational term.)
>
> These are all scalar quantities.
>
Dear Eric,
Thank you for your comment.
P(pressure) = F(force) / A(area)
F and A are two vectors being parallel to each other,
and P is a scalar quantity. Please refer to:
http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html
A parallelepiped with three vectors A,B,C form adjacent edges,
and the volume of the parallelepiped is V=abs( Ao(BXC) ). o is
dot product, and X is cross product. V is a scalar quantity.
Vd(volume density) = M(mass) / V(volume)
M, V, and Vd are scalar quantities.
Ka-In Yen
Magnetic force: Drag force and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
yen, ka-in
Einstein was ill-trained on three dimensional vector
space; the fourth dimension was suggested by him.
A BLOODY JOKE!!!
Ka-In Yen
Magnetic force: Drag and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Ka-In Yen wrote:
> The proof of mass vector.
>
...
Ka-In Yen
Dear PD, Eric Gisse,
Do you have any further questions?
Ka-In Yen
Magnetic force: Drag and Bernoulli force of ether dynamics
http://www.geocities.com/redlorikee
Ka-In Yen wrote:
> The proof of mass vector.
>
Ka-In Yen
> The proof of mass vector.
>
> Introduction:
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
>
> 1. The unit of vector.
> In physics, The unit of three-dimensional cartesian coordinate
> systems is meter. In this paper, a point of 3-D coordinate
> system is written as
> (p1,p2,p3) m, or (p:3) m
> and a vector is written as
> <a,b,c> m, or <a:3> m
> or
> l m<i,j,k> = <a,b,c> m
> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> and <i,j,k> is a unit vector which gives the direction of
> the vector.
>
> A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
> and <j:3> are unit vectors. The area vector of the parallelogram
> is the cross product of these two vectors.
> l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
> = lh abs(sin(theta)) (m^2)<k:3>
> Where theta is the angle between <i:3> and <j:3>. <k:3> is
> a unit vector which is perpendicular to <i:3> and <j:3>.
> For AXB=-BXA, an area has two directions.
> We can divide the area vector by the length vector.
> lh*abs(sin(theta))<k:3>/[l<i:3>]
> =h<i:3>X<j:3>/<i:3>
> =h(<i:3>X<j:3>)X<i:3>
> (The direction, <i:3>, is not changed by "division", and
> the division is replaced by a cross product.)
> =-h<i:3>X(<i:3>X<j:3>)
> =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
> (where o is dot product.)
> =-h(cos(theta)<i:3>-<j:3>)
> =h(<j:3>-cos(theta)<i:3>) m
> The result is a rectangle, not the original parallelogram.
In the above, the "area vector division by length vector" is suggested.
We can divide a length vector by a velocity in a different way.
Assuming
a length vector is l m<i:3>, and a velocity is v (m/s) <j:3>. <i:3> and
<j:3> are unit vectors.
l m<i:3> / [ v (m/s) <j:3> ]
=l <i:3>o<j:3> / v s
<j:3> is moved to numerator. o is dot product.
=l cos(theta) / v s ---------(1)
theta is the angle between two vectors.
OR
v (m/s)<j:3> / [ l m<i:3> ]
=v cos(theta) / l s^(-1) --------(2)
Both length vector and area vector have two directions; we can choose
one of their directions to keep cos(theta)>0.
(1)*(2)=(cos(theta))^2 (The result is not 1.)
We can caculate pressure=force/area with same method.
Ka-In Yen
Magnetic force: Drag and Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Eric Gisse
>
> In the above, the "area vector division by length vector" is suggested.
Vector division is not a defined operation for vectors.
[snip]
Ka-In Yen
> Ka-In Yen wrote:
> > The proof of mass vector.
> >
> > In physics, The unit of three-dimensional cartesian coordinate
> > systems is meter. In this paper, a point of 3-D coordinate
> > system is written as
> > (p1,p2,p3) m, or (p:3) m
> > and a vector is written as
> > <a,b,c> m, or <a:3> m
> > or
> > l m<i,j,k> = <a,b,c> m
>
> We can divide a length vector by a velocity in a different way.
> Assuming
> a length vector is l m<i:3>, and a velocity is v (m/s) <j:3>. <i:3> and
> <j:3> are unit vectors.
>
> l m<i:3> / [ v (m/s) <j:3> ]
> =l <i:3>o<j:3> / v s
> <j:3> is moved to numerator. o is dot product.
> =l cos(theta) / v s ---------(1)
> theta is the angle between two vectors.
>
> OR
>
> v (m/s)<j:3> / [ l m<i:3> ]
> =v cos(theta) / l s^(-1) --------(2)
Length vector division by velocity gives two solutions:
l cos(theta) / v s or l / (v cos(theta)) s. Depending
on your application, you choose one operation.
>
> Both length vector and area vector have two directions; we can choose
> one of their directions to keep cos(theta)>0.
Correction: It should be cos(theta)>=0.
If negative time is your application, then cos(theta)>=0 is
unnecessary.
Ka-In Yen
Dear Eric,
Thank you for your comment. Then I am the first one.
Ka-In Yen
> Eric Gisse wrote:
> > > In the above, the "area vector division by length vector" is suggested.
> >
> > Vector division is not a defined operation for vectors.
>
> Dear Eric,
> Thank you for your comment. Then I am the first one.
Mathematically I prove that Einstein was ill-trained on three
dimensional vector algebra. ^_^
Pmb
>>
>> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
>> and <i,j,k> is a unit vector which gives the direction of
>> the vector.
<i,j,k> is not a unit vector. It has a magnitude of sqrt(3)
>> 2. Linear mass density is a vector.
>>
>> The mass of a string is M kg, and the length of the string
>> is l m<i:3>. Where l m is the magnitude of the length, and
>> <i:3> is a 3-D unit vector which gives the direction of the
>> string. Then the linear mass density of the string is:
>>
>> M/(l<i:3>)=(M/l) (kg/m)<i:3>
That doesn't mean that you can call mass a vector. Mass is a scalar which
has a value at every point on the string. As you have it there are two
vectors each of which are tangent to the string and point in opposite
directions.
Pete
Ka-In Yen
Pmb wrote:
> >> l m<i,j,k> = <a,b,c> m
> >>
> >> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> >> and <i,j,k> is a unit vector which gives the direction of
> >> the vector.
>
> <i,j,k> is not a unit vector. It has a magnitude of sqrt(3)
Dear Pete,
Thank you for your comment. i=a/l, j=b/l, and k=c/l.
<i,j,k> is a unit vector.
>
> >> 2. Linear mass density is a vector.
> >>
> >> The mass of a string is M kg, and the length of the string
> >> is l m<i:3>. Where l m is the magnitude of the length, and
> >> <i:3> is a 3-D unit vector which gives the direction of the
> >> string. Then the linear mass density of the string is:
> >>
> >> M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> That doesn't mean that you can call mass a vector. Mass is a scalar which
> has a value at every point on the string. As you have it there are two
> vectors each of which are tangent to the string and point in opposite
> directions.
Vector of linear mass density and vector of surface mass
density are a long name; shortly I call them mass vector.
Sorry for the confussion. Please refer to:
http://www.geocities.com/redlorikee/mdb2.html
Ka-In Yen
Ka-In Yen
the null result of MMX; STR was based on an incomplete
physical mathematics.
Ka-In Yen
Magnetic force: Drag nd Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Ka-In Yen wrote:
> The proof of mass vector.
>
> Introduction:
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
>
> 1. The unit of vector.
>
> In physics, The unit of three-dimensional cartesian coordinate
> systems is meter. In this paper, a point of 3-D coordinate
> system is written as
>
> (p1,p2,p3) m, or (p:3) m
>
> and a vector is written as
>
> <a,b,c> m, or <a:3> m
>
> or
>
> l m<i,j,k> = <a,b,c> m
>
> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> and <i,j,k> is a unit vector which gives the direction of
> the vector.
>
> For three reasons, a magnitude of a vector can not add to a
> scalar:
> i) The magnitude belongs to the set of vector; it's a
> portion of a vector. Scalar belongs to a field.
> ii) The magnitude is real non-negative number, but scalar
> is real number.
> iii) The unit of magnitude is meter, but scalar has no unit.
> This is a major difference between physics and mathematics.
> 5m+3 is meaningless.
>
>
> 2. Linear mass density is a vector.
>
> The mass of a string is M kg, and the length of the string
> is l m<i:3>. Where l m is the magnitude of the length, and
> <i:3> is a 3-D unit vector which gives the direction of the
> string. Then the linear mass density of the string is:
>
> M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> The direction, <i:3>, is not changed by "division", so we
> can move <i:3> from denominator to numerator. A direction
> is changed by -1 only. A proof is found in Clifford algebras:
>
> [Proof]
> k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
> =(k/l) <i,j,k>
> where l is the magnitude of <a,b,c>, and <i,j,k> is the
> unit vector of <a,b,c>.
> [Proof]
>
>
> 3. Surface mass density is a vector.
>
> A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
> and <j:3> are unit vectors. The area vector of the parallelogram
> is the cross product of these two vectors.
>
> l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
> = lh abs(sin(theta)) (m^2)<k:3>
>
> Where theta is the angle between <i:3> and <j:3>. <k:3> is
> a unit vector which is perpendicular to <i:3> and <j:3>.
> For AXB=-BXA, an area has two directions.
>
> We can divide the area vector by the length vector.
>
> lh*abs(sin(theta))<k:3>/[l<i:3>]
> =h<i:3>X<j:3>/<i:3>
> =h(<i:3>X<j:3>)X<i:3>
> (The direction, <i:3>, is not changed by "division", and
> the division is replaced by a cross product.)
> =-h<i:3>X(<i:3>X<j:3>)
> =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
> (where o is dot product.)
> =-h(cos(theta)<i:3>-<j:3>)
> =h(<j:3>-cos(theta)<i:3>) m
>
Hexenmeister
"Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
news:1137987739.5...@f14g2000cwb.googlegroups.com...
> Back to 1905, Einstein was lack of a fine tool to solve
> the null result of MMX;
No he wasn't. Georges Sagnac had it built by 1913.
http://www.androcles01.pwp.blueyonder.co.uk/Sagnac.JPG
> STR was based on an incomplete
> physical mathematics.
Wrong again.
STR was based on a deliberate hoax.
http://www.androcles01.pwp.blueyonder.co.uk/how_to_be_as_smart_as_einstein.htm
>
> Ka-In Yen
> Magnetic force: Drag nd Bernoulli force of ether dynamics.
> http://www.geocities.com/redlorikee
Wrong a third time. There is no aether.
http://www.androcles01.pwp.blueyonder.co.uk/RR_C7/RelativityRevealed.htm
Notice I'm using real data.
Hexenmeister.
Ka-In Yen
Dear Hexenmeister,
Thank you for your comment. It's a high probability that a flawless
derivation has some physical meaning. If you find any flaw of the
mathematic derivation of the theory, please kindly advise me; it's
grateful.
Ka-In Yen
especially logic. Leading by Einstein, they overthrew logic.
What a bunch of lunatic idiots!!!
Ka-In Yen
Magnetic force: Drag nd Bernoulli force of ether dynamics.
http://www.geocities.com/redlorikee
Ka-In Yen wrote:
> The proof of mass vector.
>
> Introduction:
> In this paper, we will prove that linear mass density and
> surface mass density are vector, and the application of mass
> vector is presented.
>
> 1. The unit of vector.
>
> In physics, The unit of three-dimensional cartesian coordinate
> systems is meter. In this paper, a point of 3-D coordinate
> system is written as
>
> (p1,p2,p3) m, or (p:3) m
>
> and a vector is written as
>
> <a,b,c> m, or <a:3> m
>
> or
>
> l m<i,j,k> = <a,b,c> m
>
> where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
> and <i,j,k> is a unit vector which gives the direction of
> the vector.
>
> For three reasons, a magnitude of a vector can not add to a
> scalar:
> i) The magnitude belongs to the set of vector; it's a
> portion of a vector. Scalar belongs to a field.
> ii) The magnitude is real non-negative number, but scalar
> is real number.
> iii) The unit of magnitude is meter, but scalar has no unit.
> This is a major difference between physics and mathematics.
> 5m+3 is meaningless.
>
>
> 2. Linear mass density is a vector.
>
> The mass of a string is M kg, and the length of the string
> is l m<i:3>. Where l m is the magnitude of the length, and
> <i:3> is a 3-D unit vector which gives the direction of the
> string. Then the linear mass density of the string is:
>
> M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> The direction, <i:3>, is not changed by "division", so we
> can move <i:3> from denominator to numerator. A direction
> is changed by -1 only. A proof is found in Clifford algebras:
>
> [Proof]
> k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
> =(k/l) <i,j,k>
> where l is the magnitude of <a,b,c>, and <i,j,k> is the
> unit vector of <a,b,c>.
> [Proof]
>
>
> 3. Surface mass density is a vector.
>
> A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
> and <j:3> are unit vectors. The area vector of the parallelogram
> is the cross product of these two vectors.
>
> l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
> = lh abs(sin(theta)) (m^2)<k:3>
>
> Where theta is the angle between <i:3> and <j:3>. <k:3> is
> a unit vector which is perpendicular to <i:3> and <j:3>.
> For AXB=-BXA, an area has two directions.
>
> We can divide the area vector by the length vector.
>
> lh*abs(sin(theta))<k:3>/[l<i:3>]
> =h<i:3>X<j:3>/<i:3>
> =h(<i:3>X<j:3>)X<i:3>
> (The direction, <i:3>, is not changed by "division", and
> the division is replaced by a cross product.)
> =-h<i:3>X(<i:3>X<j:3>)
> =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
> (where o is dot product.)
> =-h(cos(theta)<i:3>-<j:3>)
> =h(<j:3>-cos(theta)<i:3>) m
>
Ka-In Yen
The proof of mass vector.
Ka-In Yen
yenk...@yahoo.com.tw
http://www.geocities.com/redlorikee
Ka-In Yen
Is it useful?
Bill Hobba
You can not divide by vectors.
Rest of rubbish snipped.
Bill
Eric Gisse
Ka-In Yen
Thank you for your comment.
Bill Hobba wrote:
> "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> news:1144028073.1...@j33g2000cwa.googlegroups.com...
> > Is it useful?
> > 2. Linear mass density is a vector.
> > The mass of a string is M kg, and the length of the string
> > is l m<i:3>. Where l m is the magnitude of the length, and
> > <i:3> is a 3-D unit vector which gives the direction of the
> > string. Then the linear mass density of the string is:
> >
> >
> > M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
/
> You can not divide by vectors.
Why?
Eric Gisse
Uh, because it is not a defined operaton?
What is the result from dividing the unit vector "i" by the unit vector
"j" ?
Bill Hobba
Ka-In Yen
Thank you for your comment.
Eric Gisse wrote:
> Ka-In Yen wrote:
> > Dear Bill Hobba,
> > Thank you for your comment.
> >
> > Bill Hobba wrote:
> > > "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> > > news:1144028073.1...@j33g2000cwa.googlegroups.com...
> > > > Is it useful?
> > > > 2. Linear mass density is a vector.
> > > > The mass of a string is M kg, and the length of the string
> > > > is l m<i:3>. Where l m is the magnitude of the length, and
> > > > <i:3> is a 3-D unit vector which gives the direction of the
> > > > string. Then the linear mass density of the string is:
> > > >
> > > >
> > > > M/(l<i:3>)=(M/l) (kg/m)<i:3>
> > >
> > > You can not divide by vectors.
> >
> > Why?
/
> Uh, because it is not a defined operaton?
Are we forbidden to define it?
Bill Hobba
Nope - but due the existence problem you need to demonstrate one exists
before defining it. And if memory serves me correctly a theorem says you
can't do it for 3 dimensions. You can for four but assocativty goes out
then window and higher dimensions are even more problematical. You are
welcome to try however - but to speak of a multiplicative inverse you need
to define it and demonstrate it is an inverse.
What I don't understand about your type is why with zero actual knowledge of
a subject you believe it is wrong and you can revolutionaries it.
Bill
Eric Gisse
Bill Hobba wrote:
[snip]
>
> What I don't understand about your type is why with zero actual knowledge of
> a subject you believe it is wrong and you can revolutionaries it.
People have heard the fables of how Einstein failed all his math
classes and still revolutionized physics and believe they can do the
same.
>
> Bill
Bill Hobba
"Eric Gisse" <jow...@gmail.com> wrote in message
news:1144206107.1...@t31g2000cwb.googlegroups.com...
Yea - and it is a total fable. He had a letter from his high school teacher
confirming his math was already of university standard. At uni he did not
do well because he was a lazy sod - but never actually failed. Which
instead of suggesting you don't need to study confirms you do - even a
genius like Einstein did not do well when he didn't.
Thanks
Bill
>
>>
>> Bill
>
Ka-In Yen
Bill Hobba wrote:
> "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> news:1144028073.1...@j33g2000cwa.googlegroups.com...
> >
> > The mass of a string is M kg, and the length of the string
> > is l m<i:3>. Where l m is the magnitude of the length, and
> > <i:3> is a 3-D unit vector which gives the direction of the
> > string. Then the linear mass density of the string is:
> >
> >
> > M/(l<i:3>)=(M/l) (kg/m)<i:3>
>
> You can not divide by vectors.
Dear Bill,
Can you tell me how you get the following three kind of vectors?
Current density(J) is a surface density and a vector; its unit is
A/m^2.
Electric field(E) is linear density and a vector; Its unit is V/m.
Displacement(D) is surface density and a vector; Its unit is coul/m^2.
Reference: Classical Electrodynamics(J.D. Jackson) p.820
Eric Gisse
If you have difficulties with vectors I suggest you stay far, far away
from Jackson.
Ka-In Yen
> Ka-In Yen wrote:
> > Bill Hobba wrote:
> > > "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> > > news:1144028073.1...@j33g2000cwa.googlegroups.com...
> > > > 2. Linear mass density is a vector.
> > >
> > > You can not divide by vectors.
> >
> > Dear Bill,
> > Can you tell me how you get the following three kind of vectors?
> >
> > Current density(J) is a surface density and a vector; its unit is
> > A/m^2.
> >
> > Electric field(E) is linear density and a vector; Its unit is V/m.
> >
> > Displacement(D) is surface density and a vector; Its unit is coul/m^2.
> >
> > Reference: Classical Electrodynamics(J.D. Jackson) p.820
> If you have difficulties with vectors I suggest you stay far, far away
> from Jackson.
Do not change subject; answer the question. (^_^)
Eric Gisse
The quantities are defined to be vectors and are operated on by tools
from vector analysis and calculus. You are inventing your own tools
because you have no clue what you are doing.
Ka-In Yen
Eric Gisse wrote:
> > > Ka-In Yen wrote:
> > > > Bill Hobba wrote:
> > > > > "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> > > > > news:1144028073.1...@j33g2000cwa.googlegroups.com...
> > > > > > 2. Linear mass density is a vector.
> > > > > > M/(l<i:3>)=(M/l) (kg/m)<i:3>
> > > > >
> > > > > You can not divide by vectors.
> > > >
> > > > Dear Bill,
> > > > Can you tell me how you get the following three kind of vectors?
> > > >
> > > > Current density(J) is a surface density and a vector; its unit is
> > > > A/m^2.
> > > >
> > > > Electric field(E) is linear density and a vector; Its unit is V/m.
> > > >
> > > > Displacement(D) is surface density and a vector; Its unit is coul/m^2.
> > > >
> > > > Reference: Classical Electrodynamics(J.D. Jackson) p.820
>
> from vector analysis and calculus. You are inventing your own tools
> because you have no clue what you are doing.
With Clifford's method, we can get the same result. Do you have
any strong reason to reject Clifford's method?
In 3D VECTOR algebra, we have to divide a mass by a length
VECTOR, and linear mass density is a VECTOR.
Eric Gisse
Idiot.
Ka-In Yen
> > Bill Hobba wrote:
> >> "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> >> news:1144028073.1...@j33g2000cwa.googlegroups.com...
> >> > Is it useful?
> >> > 2. Linear mass density is a vector.
> >> >
Dear Bill,
Thank you for the information you provide. You were misled by
mathematician. Mathematicians play vectors without unit(meter
for example); that's not for physicists.
Area = Length * Height
Height = Area / Length
I learned the above equations when I was a pupil in elementary
school. Dividing an area by a length, we always get the height
of a rectangle(although infinite number of parallelograms have
the same area and length).
Physicists have been doing vector-by-vector-division for a
hundred years. The equation of magnetic force is "vector division
by vector".
F=iLXB (X is corss product).
L is a length vector; assuming L=l m<i:3>, <i:3> is a unit vector.
B is magnetic flux density. Its unit is tesla, or Wb/m^2. Wb, Weber,
is the unit of magnetic flux. Assuming
B= b (Wb/m^2)<j:3>, <j:3> is a unit vector.
Since B is a vector of surface density, we can rewrite it:
B= b Wb/(m^2<j:3>), <j:3> is moved to denominator.
LXB= l m<i:3> X b (Wb/m^2)<j:3>
= l m<i:3> * b Wb /(m^2<j:3>)
= lb Wb m<i:3>/(m^2<j:3>)
It's VDV.
Eric Gisse
Ka-In Yen wrote:
> Bill Hobba wrote:
> > "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> > news:1144112932.8...@i39g2000cwa.googlegroups.com...
> > > Bill Hobba wrote:
> > >> "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
> > >> news:1144028073.1...@j33g2000cwa.googlegroups.com...
> > >> > Is it useful?
> > >> > 2. Linear mass density is a vector.
> > >> >
> > >> > M/(l<i:3>)=(M/l) (kg/m)<i:3>
> > >> You can not divide by vectors.
> > > Why?
> >
> > http://www.mcasco.com/qa_vdq.html
>
> Dear Bill,
>
> Thank you for the information you provide. You were misled by
> mathematician. Mathematicians play vectors without unit(meter
> for example); that's not for physicists.
A meter is a length, not a direction. You have no idea what you are
talking about.
[snip idiocy]
Bilge
>With Clifford's method, we can get the same result.
No, you don't. Feel free to write down the expression in terms of
the clifford algebra.
>Do you have any strong reason to reject Clifford's method?
>In 3D VECTOR algebra, we have to divide a mass by a length
>VECTOR, and linear mass density is a VECTOR.
Wrong. Given a linear mass density lying along -a < x < a, what
direction does it point?
Bilge
>Bill Hobba wrote:
>> "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
>> news:1144112932.8...@i39g2000cwa.googlegroups.com...
>> > Bill Hobba wrote:
>> >> "Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
>> >> news:1144028073.1...@j33g2000cwa.googlegroups.com...
>> >> > Is it useful?
>> >> > 2. Linear mass density is a vector.
>> >> >
>> >> > M/(l<i:3>)=(M/l) (kg/m)<i:3>
>> >> You can not divide by vectors.
>> > Why?
>>
>> http://www.mcasco.com/qa_vdq.html
>
>Dear Bill,
>
>Thank you for the information you provide. You were misled by
>mathematician. Mathematicians play vectors without unit(meter
>for example); that's not for physicists.
Well, I'm a physicist and as far as I can tell, you haven't yet
said anything that makes an physical sense, regardless of what you
want to claim about mathematics.
> Area = Length * Height
> Height = Area / Length
>
>I learned the above equations when I was a pupil in elementary
>school. Dividing an area by a length, we always get the height
>of a rectangle(although infinite number of parallelograms have
>the same area and length).
What does that have to do with dividing by vectors? All you wrote
were magnitudes.
>Physicists have been doing vector-by-vector-division for a
>hundred years. The equation of magnetic force is "vector division
>by vector".
No, it is not.
>F=iLXB (X is corss product).
Note that L is a vector and B is a pseudovector and those are
not dividing anything.
Ka-In Yen
Thank you for your comment.
Bilge wrote:
> Ka-In Yen:
> >
> >With Clifford's method, we can get the same result.
>
> No, you don't. Feel free to write down the expression in terms of
> the clifford algebra.
>
Clifford proves k / <a,b,c> = k<a,b,c> / <a,b,c>^2
[Proof]
k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
=(k/l) <i,j,k>
where l=sqrt(a^2+b^2+c^2) is the magnitude of <a,b,c>,
and <i,j,k>=<a,b,c>/l is the unit vector of <a,b,c>.
[End of proof]
> >Do you have any strong reason to reject Clifford's method?
>
> >In 3D VECTOR algebra, we have to divide a mass by a length
> >VECTOR, and linear mass density is a VECTOR.
>
> Wrong. Given a linear mass density lying along -a < x < a, what
> direction does it point?
We are talking about 3D vector algebra, your question is 1D.
two points : (-a, y, z) m and (a, y, z) m (m is meter).
length vector: (a,y,z)m - (-a,y,z)m = <2a,0,0>m
mass of a straight wire between the above two points is M kg.
linear mass density = M kg / <2a,0,0>m
= (M/2a) <1,0,0> kg/m
Bilge
>Thank you for your comment.
>
>Bilge wrote:
>> Ka-In Yen:
>> >
>> >With Clifford's method, we can get the same result.
>>
>> No, you don't. Feel free to write down the expression in terms of
>> the clifford algebra.
>>
>
>Clifford proves k / <a,b,c> = k<a,b,c> / <a,b,c>^2
Define your notation.
>[Proof]
> k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
> =(k/l) <i,j,k>
> where l=sqrt(a^2+b^2+c^2) is the magnitude of <a,b,c>,
>and <i,j,k>=<a,b,c>/l is the unit vector of <a,b,c>.
>[End of proof]
>
>> >Do you have any strong reason to reject Clifford's method?
>>
>> >In 3D VECTOR algebra, we have to divide a mass by a length
>> >VECTOR, and linear mass density is a VECTOR.
>>
>> Wrong. Given a linear mass density lying along -a < x < a, what
>> direction does it point?
>
>We are talking about 3D vector algebra, your question is 1D.
Oh, in other words, wires don't exist in 3-d?
Ka-In Yen
Thank you for your comment.
Bilge wrote:
> Ka-In Yen:
> >Bill Hobba wrote:
> >> http://www.mcasco.com/qa_vdq.html
> >Thank you for the information you provide. You were misled by
> >mathematician. Mathematicians play vectors without unit(meter
> >for example); that's not for physicists.
> Well, I'm a physicist and as far as I can tell, you haven't yet
> said anything that makes an physical sense, regardless of what you
> want to claim about mathematics.
> > Area = Length * Height
> > Height = Area / Length
> >
> >I learned the above equations when I was a pupil in elementary
> >school. Dividing an area by a length, we always get the height
> >of a rectangle(although infinite number of parallelograms have
> >the same area and length).
>
> What does that have to do with dividing by vectors? All you wrote
> were magnitudes.
According to mathematician's opinion:
"Again there are two unknowns, |V| and u, in the equation so there are
infinitely many answers. Therefore cross division is also undefined."
---- http://www.mcasco.com/qa_vdq.html
That's not true. Stupid mathematicians hinder the development
of 3D vector algebra.
An area vector is A<i:3>m^2, and its length is l<j:3>m.
where <i:3> and <j:3> are unit vectors and m is meter.
We can divide the area vector by the length vector, and
we get the height(vector) of rectangle.
A<i:3>m^2 / l<j:3>m
=(A/l) <i:3>x<j:3> m (x is cross product)
=(A*sin(theta)/l) <k:3> m (<k:3>=(<i:3>x<j:3>)/sin(theta))
where theta is the angle between <i:3> and <j:3>.
<k:3> is a unit vector and perpendicular to <i:3> and <j:3>.
Or
A<i:3>m^2 / l<j:3>m
=A/(l <i:3>x<j:3>) m
=A/(l*sin(theta)) <k:3> m
>
> >Physicists have been doing vector-by-vector-division for a
> >hundred years. The equation of magnetic force is "vector division
> >by vector".
>
> No, it is not.
>
> >F=iLXB (X is corss product).
>
> Note that L is a vector and B is a pseudovector and those are
> not dividing anything.
As soon as you accept Clifford's method, you will realize that
LXB is vector by vector division.
Eric Gisse
Only a crank complains about "stupid mathematicians".
[snip]
Yet for all your idiotic notation, you are unable to demonstrate that
your vector "division" has an inverse.
Bilge
>According to mathematician's opinion:
>"Again there are two unknowns, |V| and u, in the equation so there are
>infinitely many answers. Therefore cross division is also undefined."
> ---- http://www.mcasco.com/qa_vdq.html
>
>That's not true.
Sure it is. There are infinitely many ways to define the vectors
A and B such that the cross product is the same.
>Stupid mathematicians hinder the development of 3D vector algebra.
No, stupid people simply don't bother to stop and think before
declaring that thousands of mathematicians are stupid.
>An area vector is A<i:3>m^2, and its length is l<j:3>m.
>where <i:3> and <j:3> are unit vectors and m is meter.
>We can divide the area vector by the length vector, and
>we get the height(vector) of rectangle.
The cross product of two vectors is a pseudovector.
>A<i:3>m^2 / l<j:3>m
>=(A/l) <i:3>x<j:3> m (x is cross product)
>=(A*sin(theta)/l) <k:3> m (<k:3>=(<i:3>x<j:3>)/sin(theta))
>where theta is the angle between <i:3> and <j:3>.
><k:3> is a unit vector and perpendicular to <i:3> and <j:3>.
I'm not about to sort out your silly notation.
>
>As soon as you accept Clifford's method, you will realize that
>LXB is vector by vector division.
Do yourself a favor. Purchase a copy of ``Clifford Algebras and
Spinors,'' Perti Lounesto.
Ka-In Yen
Bilge wrote:
> Ka-In Yen:
> >A<i:3>m^2 / l<j:3>m
> >=(A/l) <i:3>x<j:3> m (x is cross product)
> >=(A*sin(theta)/l) <k:3> m (<k:3>=(<i:3>x<j:3>)/sin(theta))
> >where theta is the angle between <i:3> and <j:3>.
> ><k:3> is a unit vector and perpendicular to <i:3> and <j:3>.
>
> I'm not about to sort out your silly notation.
I have define the notation in my paper. If you do not read
my paper, how can you comment on my paper?
Bilge
I'm commenting on the article you posted. This is a newsgroup, not
a journal.
Ka-In Yen
Bilge wrote:
> Ka-In Yen:
>
> >According to mathematician's opinion:
> >"Again there are two unknowns, |V| and u, in the equation so there are
> >infinitely many answers. Therefore cross division is also undefined."
> > ---- http://www.mcasco.com/qa_vdq.html
> >
> >That's not true.
>
> Sure it is. There are infinitely many ways to define the vectors
> A and B such that the cross product is the same.
Although there are infinite solutions, but we are not forbidden
to find a specific solution.
> >
> >As soon as you accept Clifford's method, you will realize that
> >LXB is vector by vector division.
>
> Do yourself a favor. Purchase a copy of ``Clifford Algebras and
> Spinors,'' Perti Lounesto.
Inverse of a vector is widely accepted by mathematicians and
physicists.
A^(-1) = 1/A = A/A^2 (where A is a vector)
Please refer to: http://en.wikipedia.org/wiki/Geometric_algebra
Bilge
>Bilge wrote:
>> Ka-In Yen:
>>
>> >According to mathematician's opinion:
>> >"Again there are two unknowns, |V| and u, in the equation so there are
>> >infinitely many answers. Therefore cross division is also undefined."
>> > ---- http://www.mcasco.com/qa_vdq.html
>> >
>> >That's not true.
>>
>> Sure it is. There are infinitely many ways to define the vectors
>> A and B such that the cross product is the same.
>
>Although there are infinite solutions, but we are not forbidden
>to find a specific solution.
What's your point?
>> >
>> >As soon as you accept Clifford's method, you will realize that
>> >LXB is vector by vector division.
>>
>> Do yourself a favor. Purchase a copy of ``Clifford Algebras and
>> Spinors,'' Perti Lounesto.
>
>Inverse of a vector is widely accepted by mathematicians and
>physicists.
You said ``division by a vector.'' Don't change the subject.
>A^(-1) = 1/A = A/A^2 (where A is a vector)
Note that the denominator is a scalar.
Ka-In Yen
Bilge wrote:
> Ka-In Yen:
> >Bilge wrote:
> >> Ka-In Yen:
> >> >LXB is vector by vector division.
> >>
> >> Do yourself a favor. Purchase a copy of ``Clifford Algebras and
> >> Spinors,'' Perti Lounesto.
> >
> >Inverse of a vector is widely accepted by mathematicians and
> >physicists.
>
> You said ``division by a vector.'' Don't change the subject.
>
Yesterday, I studied quaternion; Hamilton had defined vector
division.
Q=A/B (Q is quaternion. A and B are two vectors.)
Q.w = A dot B / B^2 ----- (3)
Q.v = AXB / B^2 ----- (4)
Please refer to:
http://www.euclideanspace.com/maths/algebra/vectors/inverse/forum2.htm
Equation (3) is applied to divide a length vector(L) by a velocity(V).
L/V = (L dot V) / V^2 or
L/V = L^2 / (L dot V)
Equation (4) is applied to divide an area vector(A) by a length
vector(L).
A/L = AXL / L^2 or
A/L = A^2 / AXL
You may find the above applications in this thread.
Bilge
>
>Bilge wrote:
>> Ka-In Yen:
>> >Bilge wrote:
>> >> Ka-In Yen:
>> >> >As soon as you accept Clifford's method, you will realize that
>> >> >LXB is vector by vector division.
>> >>
>> >> Do yourself a favor. Purchase a copy of ``Clifford Algebras and
>> >> Spinors,'' Perti Lounesto.
>> >
>> >Inverse of a vector is widely accepted by mathematicians and
>> >physicists.
>>
>> You said ``division by a vector.'' Don't change the subject.
>>
>
>Yesterday, I studied quaternion; Hamilton had defined vector
>division.
yen, ka-in
Bilge wrote:
> Ka-In Yen:
> >
> >Bilge wrote:
> >> Ka-In Yen:
> >> >Bilge wrote:
> >> >> Ka-In Yen:
> >> >> >As soon as you accept Clifford's method, you will realize that
> >> >> >LXB is vector by vector division.
> >> >>
> >> >> Do yourself a favor. Purchase a copy of ``Clifford Algebras and
> >> >> Spinors,'' Perti Lounesto.
> >> >
> >> >Inverse of a vector is widely accepted by mathematicians and
> >> >physicists.
> >>
> >> You said ``division by a vector.'' Don't change the subject.
> >>
> >
> >Yesterday, I studied quaternion; Hamilton had defined vector
> >division.
>
> You said ``division by a vector.'' Stop changing the subject.
Now, you are well-trained in 3D vector algebra BY ME. ^_^
Ka-In Yen
Einstein's FOUR dimensional space-time, but they are ill-trained
in THREE dimensional vector algebra. WHAT A BLOODY JOKE!!!
The proof of mass vector.
Ka-In Yen
http://www.geocities.com/redlorikee
Introduction:
In this paper, we will prove that linear mass density and
surface mass density are vector, and the application of mass
vector is presented.
1. The unit of vector.
In physics, The unit of three-dimensional cartesian coordinate
systems is meter. In this paper, a point of 3-D coordinate
system is written as
(p1,p2,p3) m, or (p:3) m
and a vector is written as
<a,b,c> m, or <a:3> m
or
l m<i,j,k> = <a,b,c> m
where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector,
and <i,j,k> is a unit vector which gives the direction of
the vector.
For three reasons, a magnitude of a vector can not add to a
scalar:
i) The magnitude belongs to the set of vector; it's a
portion of a vector. Scalar belongs to a field.
ii) The magnitude is real non-negative number, but scalar
is real number.
iii) The unit of magnitude is meter, but scalar has no unit.
This is a major difference between physics and mathematics.
5m+3 is meaningless.
2. Linear mass density is a vector.
The mass of a string is M kg, and the length of the string
is l m<i:3>. Where l m is the magnitude of the length, and
<i:3> is a 3-D unit vector which gives the direction of the
string. Then the linear mass density of the string is:
M/(l<i:3>)=(M/l) (kg/m)<i:3>
The direction, <i:3>, is not changed by "division", so we
can move <i:3> from denominator to numerator. A direction
is changed by -1 only. A proof is found in Clifford algebras:
[Proof]
k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2]
=(k/l) <i,j,k>
where l is the magnitude of <a,b,c>, and <i,j,k> is the
unit vector of <a,b,c>.
[Proof]
3. Surface mass density is a vector.
A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3>
and <j:3> are unit vectors. The area vector of the parallelogram
is the cross product of these two vectors.
l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3>
= lh abs(sin(theta)) (m^2)<k:3>
Where theta is the angle between <i:3> and <j:3>. <k:3> is
a unit vector which is perpendicular to <i:3> and <j:3>.
For AXB=-BXA, an area has two directions.
We can divide the area vector by the length vector.
lh*abs(sin(theta))<k:3>/[l<i:3>]
=h<i:3>X<j:3>/<i:3>
=h(<i:3>X<j:3>)X<i:3>
(The direction, <i:3>, is not changed by "division", and
the division is replaced by a cross product.)
=-h<i:3>X(<i:3>X<j:3>)
=-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)]
(where o is dot product.)
=-h(cos(theta)<i:3>-<j:3>)
=h(<j:3>-cos(theta)<i:3>) m
The result is a rectangle, not the original parallelogram. We
can test the result.
h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3>
The magnitude of the area vector is conserved, but the direction
is opposite.
The mass of a round plate is M kg, and the area vector is
A m^2<i:3>; then the surface mass density is
M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3>
4. Mass vector in physics.
Mass vector has been found in two equations: 1) the velocity
equation of string. 2) Bernoulli's equation.
i) For waves on a string, we have the velocity equation:
v=sqrt(tau/mu). v is velocity of wave, tau is tension
applying to string, and mu is linear mass density of
string. We can rewrite the equation:
mu=tau/v^2.
In the above equation, the mu is parallel to tau, and both
of them are vector.
ii) Bernoulli's equation is:
P + k*v^2/2=C (P is pressure, k is volume density, and v is
velocity. Here we neglect the gravitational term.)
Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's
equation(where <i:3> is a unit vector),
P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3>
F<i:3> + L<i:3>*v^2/2=C*A<i:3>
(where F is the magnitude of force, and L is the magnitude
of linear mass density.)
These two equations are well used in the theory "Magnetic force:
Combining Drag force and Bernoulli force of ether dynamics."
For detail, please refer to my site:
http://www.geocities.com/redlorikee
Golden Boar
There is no mass, it is just an illusion created by frequency.
What you think of as rest mass is simply:
m = fC.h / c^2
fC is the Compton frequency,
h is Planck's constant,
c is the speed of light.
yen, ka-in
Any further questions?
Bilge
>
>Any further questions?
Just one. Why do you persist in posting this crap?
yen, ka-in
Bilge wrote:
> yen, ka-in:
> >
> >Any further questions?
>
> Just one. Why do you persist in posting this crap?
Do you mean that Clifford is crap, and Hamilton is crap?
Bilge
Is your name clifford and hamilton? If not, don't blame someone
else for the crap you post.
Ka-In Yen
If you do not read my paper, how can you comment on my paper?
It's not a responsible comment.
Bilge
Go back and reread the previous replies to the same garbage.
>It's not a responsible comment.
Then, make a responsible one.
Ka-In Yen
Bilge wrote:
> Ka-In Yen:
> >
> >Bilge wrote:
> >> yen, ka-in:
> >> >
> >> >Bilge wrote:
> >> >> yen, ka-in:
> >> >> >
> >> >> >Any further questions?
> >> >>
> >> >> Just one. Why do you persist in posting this crap?
> >> >
> >> >Do you mean that Clifford is crap, and Hamilton is crap?
> >>
> >> Is your name clifford and hamilton? If not, don't blame someone
> >> else for the crap you post.
> >
> >If you do not read my paper, how can you comment on my paper?
>
> Go back and reread the previous replies to the same garbage.
>
For your reference: vector division in Matlab.
http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
Ka-In Yen
Ka-In Yen wrote:
> Bilge wrote:
> > Ka-In Yen:
> > >
> > >Bilge wrote:
> > >> yen, ka-in:
> > >> >
> > >> >Bilge wrote:
> > >> >> yen, ka-in:
> > >> >> >
> > >> >> >Any further questions?
> > >> >>
> > >> >> Just one. Why do you persist in posting this crap?
> > >> >
> > >> >Do you mean that Clifford is crap, and Hamilton is crap?
> > >>
> > >> Is your name clifford and hamilton? If not, don't blame someone
> > >> else for the crap you post.
> > >
> > >If you do not read my paper, how can you comment on my paper?
> >
> > Go back and reread the previous replies to the same garbage.
> >
>
For your reference: vector division in Matlab.
Please try this one:
http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
> http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
Phineas T Puddleduck
Ka-In Yen <yen...@yahoo.com.tw> wrote:
What does the direction in a mass vector represent?
--
The greatest enemy of science is pseudoscience.
Jaffa cakes. Sweet delicious orangey jaffa goodness, and an abject lesson why
parroting information from the web will not teach you cosmology.
Official emperor of sci.physics, head mumbler of the "Cult of INSANE SCIENCE".
Please pay no attention to my butt poking forward, it is expanding.
Relf's Law?
"Bullshit repeated to the limit of infinity asymptotically approaches
the odour of roses."
--
Posted via a free Usenet account from http://www.teranews.com
Eric Gisse
Ka-In Yen wrote:
[...]
>
> For your reference: vector division in Matlab.
>
> http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
Worthless. Using the method MATLAB uses, there are an infinite number
of matricies that a and b that create the product a/b.
You repost the same tripe about once a month in the same thread over
and over while ignoring criticisms that would cause you to have to
abandon your work.
Ka-In Yen
Phineas T Puddleduck wrote:
> In article <1151625795.9...@x69g2000cwx.googlegroups.com>,
> Ka-In Yen <yen...@yahoo.com.tw> wrote:
>
> > Ka-In Yen wrote:
> > > Bilge wrote:
> > > > Ka-In Yen:
> > > > >
> > > > >Bilge wrote:
> > > > >> yen, ka-in:
> > > > >> >
> > > > >> >Bilge wrote:
> > > > >> >> yen, ka-in:
> > > > >> >> >
> > > > >> >> >Any further questions?
> > > > >> >>
> > > > >> >> Just one. Why do you persist in posting this crap?
> > > > >> >
> > > > >> >Do you mean that Clifford is crap, and Hamilton is crap?
> > > > >>
> > > > >> Is your name clifford and hamilton? If not, don't blame someone
> > > > >> else for the crap you post.
> > > > >
> > > > >If you do not read my paper, how can you comment on my paper?
> > > >
> > > > Go back and reread the previous replies to the same garbage.
> > > >
> > >
> >
> > For your reference: vector division in Matlab.
> >
> > Please try this one:
> > http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
> >
> > > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
> >
>
>
> What does the direction in a mass vector represent?
In 3D vector algebra, we have to divide a mass by a length vector; so
the linear mass density is a vector, and its direction is same to the
length vector.
Eric Gisse
Division is not a defined operation in Euclidian vector analysis.
...and LENGTH IS NOT A VECTOR, IT IS A SCALAR.
Ka-In Yen
Eric Gisse wrote:
> Ka-In Yen wrote:
>
> [...]
>
> >
> > For your reference: vector division in Matlab.
> >
> > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
>
> Worthless. Using the method MATLAB uses, there are an infinite number
> of matricies that a and b that create the product a/b.
Obviously you did not read Titus's posting carefully. Please try again:
http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
> You repost the same tripe about once a month in the same thread over
> and over while ignoring criticisms that would cause you to have to
> abandon your work.
Home work for Eric Gisse:
A rectangle sits in 3D space. The area vector of the rectangle is A,
and the legth vector of one side of the rectangle is L. Please find
the length vector of the other side of the rectangle?
Phineas T Puddleduck
Ka-In Yen <yen...@yahoo.com.tw> wrote:
Are you truly this clueless?
--
The greatest enemy of science is pseudoscience.
e=pc and p=hk
Eric Gisse
Ka-In Yen wrote:
> Eric Gisse wrote:
> > Ka-In Yen wrote:
> >
> > [...]
> >
> > >
> > > For your reference: vector division in Matlab.
> > >
> > > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
> >
> > Worthless. Using the method MATLAB uses, there are an infinite number
> > of matricies that a and b that create the product a/b.
>
> Obviously you did not read Titus's posting carefully. Please try again:
>
> http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
What part of "underdetermined" confuses you?
Vector division is not defined at all, much less that way, because
there is no unique inverse!
>
>
>
> > You repost the same tripe about once a month in the same thread over
> > and over while ignoring criticisms that would cause you to have to
> > abandon your work.
>
> Home work for Eric Gisse:
> A rectangle sits in 3D space. The area vector of the rectangle is A,
> and the legth vector of one side of the rectangle is L. Please find
> the length vector of the other side of the rectangle?
LENGTH IS NOT A VECTOR.
AREA IS NOT A VECTOR.
Bilge
>
>Ka-In Yen wrote:
>> Bilge wrote:
>> > Ka-In Yen:
>> > >
>> > >Bilge wrote:
>> > >> yen, ka-in:
>> > >> >
>> > >> >Bilge wrote:
>> > >> >> yen, ka-in:
>> > >> >> >
>> > >> >> >Any further questions?
>> > >> >>
>> > >> >> Just one. Why do you persist in posting this crap?
>> > >> >
>> > >> >Do you mean that Clifford is crap, and Hamilton is crap?
>> > >>
>> > >> Is your name clifford and hamilton? If not, don't blame someone
>> > >> else for the crap you post.
>> > >
>> > >If you do not read my paper, how can you comment on my paper?
>> >
>> > Go back and reread the previous replies to the same garbage.
>> >
>>
>
>For your reference: vector division in Matlab.
Since I don't have matlab, I really don't care what sorts
of pseudo-operations matlab defines as a convenience.
Bilge
>Ka-In Yen <yen...@yahoo.com.tw> wrote:
>
>> Ka-In Yen wrote:
>> > Bilge wrote:
>> > > Ka-In Yen:
>> > > >
>> > > >Bilge wrote:
>> > > >> yen, ka-in:
>> > > >> >
>> > > >> >Bilge wrote:
>> > > >> >> yen, ka-in:
>> > > >> >> >
>> > > >> >> >Any further questions?
>> > > >> >>
>> > > >> >> Just one. Why do you persist in posting this crap?
>> > > >> >
>> > > >> >Do you mean that Clifford is crap, and Hamilton is crap?
>> > > >>
>> > > >> Is your name clifford and hamilton? If not, don't blame someone
>> > > >> else for the crap you post.
>> > > >
>> > > >If you do not read my paper, how can you comment on my paper?
>> > >
>> > > Go back and reread the previous replies to the same garbage.
>> > >
>> >
>>
>> For your reference: vector division in Matlab.
>>
>> Please try this one:
>> http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
>>
>> > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
>>
>
>
>What does the direction in a mass vector represent?
I already tried that one on him. My guess is that it points
to where the sun doesn't shine.
Bilge
>Phineas T Puddleduck wrote:
[...]
>> What does the direction in a mass vector represent?
>
>In 3D vector algebra, we have to divide a mass by a length vector; so
>the linear mass density is a vector, and its direction is same to the
>length vector.
You need a remedial course in vector algebra. Length is a scalar.
The length of a vector, V is defined by L = sqrt(V.V). A linear
mass density is a scalar.
Ka-In Yen
Phineas T Puddleduck wrote:
> In article <1151713860.4...@p79g2000cwp.googlegroups.com>,
> Ka-In Yen <yen...@yahoo.com.tw> wrote:
>
> > Eric Gisse wrote:
> > > Ka-In Yen wrote:
> > >
> > > [...]
> > >
> > > >
> > > > For your reference: vector division in Matlab.
> > > >
> > > > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
> > >
> > > Worthless. Using the method MATLAB uses, there are an infinite number
> > > of matricies that a and b that create the product a/b.
> >
> > Obviously you did not read Titus's posting carefully. Please try again:
> >
> > http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
> >
> >
> >
> > > You repost the same tripe about once a month in the same thread over
> > > and over while ignoring criticisms that would cause you to have to
> > > abandon your work.
> >
> > Home work for Eric Gisse:
> > A rectangle sits in 3D space. The area vector of the rectangle is A,
> > and the legth vector of one side of the rectangle is L. Please find
> > the length vector of the other side of the rectangle?
> >
>
> Are you truly this clueless?
The answer is in this thread.
Ka-In Yen
Length-vector is a vector.
>
> AREA IS NOT A VECTOR.
For your reference:
Eric Gisse
I suppose that is true...
Eric Gisse
Ka-In Yen wrote:
> Eric Gisse wrote:
> > Ka-In Yen wrote:
> > > Eric Gisse wrote:
> > > > Ka-In Yen wrote:
> > > >
> > > > [...]
> > > >
> > > > >
> > > > > For your reference: vector division in Matlab.
> > > > >
> > > > > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
> > > >
> > > > Worthless. Using the method MATLAB uses, there are an infinite number
> > > > of matricies that a and b that create the product a/b.
> > >
> > > Obviously you did not read Titus's posting carefully. Please try again:
> > >
> > > http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
> >
> > What part of "underdetermined" confuses you?
> >
> > Vector division is not defined at all, much less that way, because
> > there is no unique inverse!
I notice this has gone uncommented.
> >
> > >
> > >
> > >
> > > > You repost the same tripe about once a month in the same thread over
> > > > and over while ignoring criticisms that would cause you to have to
> > > > abandon your work.
> > >
> > > Home work for Eric Gisse:
> > > A rectangle sits in 3D space. The area vector of the rectangle is A,
> > > and the legth vector of one side of the rectangle is L. Please find
> > > the length vector of the other side of the rectangle?
> >
> > LENGTH IS NOT A VECTOR.
>
> Length-vector is a vector.
Length is a scalar, you stupid fuck. A vector has magnitude (length)
and direction.
>
> >
> > AREA IS NOT A VECTOR.
>
> For your reference:
>
> http://en.wikipedia.org/wiki/Vector_area
Try referencing things that are actually relevant.
Ka-In Yen
Eric Gisse wrote:
> Ka-In Yen wrote:
> > Eric Gisse wrote:
> > > Ka-In Yen wrote:
> > > > Eric Gisse wrote:
> > > > > Ka-In Yen wrote:
> > > > >
> > > > > [...]
> > > > >
> > > > > >
> > > > > > For your reference: vector division in Matlab.
> > > > > >
> > > > > > http://newsreader.mathworks.com/WebX?1...@88.ug0LaenUYOM.0@.ef097af
> > > > >
> > > > > Worthless. Using the method MATLAB uses, there are an infinite number
> > > > > of matricies that a and b that create the product a/b.
> > > >
> > > > Obviously you did not read Titus's posting carefully. Please try again:
> > > >
> > > > http://www.google.com/search?hl=en&lr=&q=%22vector+division+in+matlab%22
> > >
> > > What part of "underdetermined" confuses you?
> > >
> > > Vector division is not defined at all, much less that way, because
> > > there is no unique inverse!
>
> I notice this has gone uncommented.
>
Do'nt waste time to find inverse of cross product, it's impossible.
To find inverse of cross product, you have to find identity first.
To any vector A, we have
AXI = A (where I is the identity of cross product.)
Unfortunately, the above equation is totally impossible to solve.
So there is no identity of cross product, and there is no inverse
of cross product. This is an intrinsic property of cross product,
and also dot product.
But Clifford proves the inverse of a vector:
A^(-1) = 1/A = A/A^2
> > >
> > > >
> > > >
> > > >
> > > > > You repost the same tripe about once a month in the same thread over
> > > > > and over while ignoring criticisms that would cause you to have to
> > > > > abandon your work.
> > > >
> > > > Home work for Eric Gisse:
> > > > A rectangle sits in 3D space. The area vector of the rectangle is A,
> > > > and the legth vector of one side of the rectangle is L. Please find
> > > > the length vector of the other side of the rectangle?
> > >
> > > LENGTH IS NOT A VECTOR.
> >
> > Length-vector is a vector.
>
> Length is a scalar, you stupid fuck. A vector has magnitude (length)
> and direction.
You call it "vector", and I call it "length-vector"; that's for
classifying:
length-vector and area-vector.
>
> >
> > >
> > > AREA IS NOT A VECTOR.
> >
> > For your reference:
> >
> > http://en.wikipedia.org/wiki/Vector_area
>
> Try referencing things that are actually relevant.
Area vector is chinilish(chinese-english). It's my bad, my
english is not so well. Area vector(chinilish) is same to
vector area(english).
Eric Gisse
Ka-In Yen wrote:
[...]
>
> A^(-1) = 1/A = A/A^2
VECTOR DIVISION IS *NOT* A DEFINED OPERATION!
[...]
>
> Area vector is chinilish(chinese-english). It's my bad, my
> english is not so well. Area vector(chinilish) is same to
> vector area(english).
It is neither the fault of Chinese (which Chinese? There is a bunch)
nor English that you do not know what you are talking about.
Ka-In Yen
Eric Gisse wrote:
> Ka-In Yen wrote:
>
> [...]
>
> >
> > A^(-1) = 1/A = A/A^2
>
> VECTOR DIVISION IS *NOT* A DEFINED OPERATION!
>
Hamilton had defined vector divisoion in 1845. I had posted
this message before.
> [...]
>
> >
> > Area vector is chinilish(chinese-english). It's my bad, my
> > english is not so well. Area vector(chinilish) is same to
> > vector area(english).
>
> It is neither the fault of Chinese (which Chinese? There is a bunch)
> nor English that you do not know what you are talking about.
Please read the following page:
http://en.wikipedia.org/wiki/Cross_product
and you will find:
"It is defined as the vector which is perpendicular
to both a and b with a magnitude equal to the
area of the parallelogram they span."
This is what I am talking about.
Ka-In Yen
Ka-In Yen
Bilge wrote:
> Ka-In Yen, crackpot of the day:
>
> >Phineas T Puddleduck wrote:
> [...]
> >> What does the direction in a mass vector represent?
> >
> >In 3D vector algebra, we have to divide a mass by a length vector; so
> >the linear mass density is a vector, and its direction is same to the
> >length vector.
>
> You need a remedial course in vector algebra.
Stupid physicists have been doing vector by vector division
for a hundred years. They need a remedial course in vector
algebra, not me.
> A linear mass density is a scalar.
That's not 3D vector algebra.
Phineas T Puddleduck
Ka-In Yen <yen...@yahoo.com.tw> wrote:
> Stupid physicists have been doing vector by vector division
> for a hundred years. They need a remedial course in vector
> algebra, not me.
>
> > A linear mass density is a scalar.
>
> That's not 3D vector algebra.
http://mathworld.wolfram.com/VectorDivision.html
There is no unique solution A to the matrix equation y=Ax unless x is
parallel to y, in which case A is a scalar. Therefore, vector division
is not defined.
http://www.mcasco.com/qa_vdq.html
Division may be thought of as unmultiplying...you know, find the number
which when multiplied by 3 yields 6. In this example the answer is
obviously 2. In vectors there are two ways of multiplying, the dot
product and the cross product. Vector division then should either undot
a vector and a scalar or uncross a pair of vectors.
The difficulty is that there are more than one vector that when dotted
with (a,b) yields 6, for example. We know this because the dot product
of (a,b)(c,d) is ac+bd=6. If we know a and b there are still two
unknowns in the equation ac+bd=6. Any pair if numbers which satisfy
this equation would qualify as the quotient of 6/(a,b). Therefore dot
division is not defined. Likewise there are infinitely many vectors
which when crossed with (a,b,c) give us (d,e,f). Consider that
AXB=C=|A||B|sin(q), where q is the angle from A to B. Any vector V in
the plane of A and B where |V|sin(u)=|B|sin(q) will yield the same
cross product. Again there are two unknowns, |V| and u, in the equation
so there are infinitely many answers. Therefore cross division is also
undefined.
--
Relf's Law? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
"Bullshit repeated to the limit of infinity asymptotically approaches
the odour of roses."
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Jaffa cakes. Sweet delicious orangey jaffa goodness, and an abject lesson why
parroting information from the web will not teach you cosmology.
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Official emperor of sci.physics, head mumbler of the "Cult of INSANE SCIENCE".
Please pay no attention to my butt poking forward, it is expanding.
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
PWNER of Vert and TomGee since 2006
"I don't know that much math." - tomgee; 2 April 2006
"I don't claim to know what I'm talking about" - tomgee; 10 May 2006
PWNED
"Puddlefuck tou are on my kill file. Good bye" - Vert admits he cannot
calculate \gamma for a photon and admits defeat - 2nd July 2006
PWNED
Eric Gisse
Ka-In Yen wrote:
> Eric Gisse wrote:
> > Ka-In Yen wrote:
> >
> > [...]
> >
> > >
> > > A^(-1) = 1/A = A/A^2
> >
> > VECTOR DIVISION IS *NOT* A DEFINED OPERATION!
> >
>
> Hamilton had defined vector divisoion in 1845. I had posted
> this message before.
Good for you. Why don't you look at the previous responses to the times
you have pointed this out, and look at the responses given to you
today.
>
> > [...]
> >
> > >
> > > Area vector is chinilish(chinese-english). It's my bad, my
> > > english is not so well. Area vector(chinilish) is same to
> > > vector area(english).
> >
> > It is neither the fault of Chinese (which Chinese? There is a bunch)
> > nor English that you do not know what you are talking about.
>
> Please read the following page:
> http://en.wikipedia.org/wiki/Cross_product
I know what the cross product is.
>
> and you will find:
>
> "It is defined as the vector which is perpendicular
> to both a and b with a magnitude equal to the
> area of the parallelogram they span."
>
> This is what I am talking about.
MAGNITUDE IS A SCALAR.
Goddamn you are stupid. Go read a book that covers vector analysis and
stop inventing idiotic terminology.
mme...@cars3.uchicago.edu
>In article <1152058227.2...@a14g2000cwb.googlegroups.com>,
>Ka-In Yen <yen...@yahoo.com.tw> wrote:
>
>> Stupid physicists have been doing vector by vector division
>> for a hundred years. They need a remedial course in vector
>> algebra, not me.
>>
>> > A linear mass density is a scalar.
>>
>> That's not 3D vector algebra.
>
>
>There is no unique solution A to the matrix equation y=Ax unless x is
>parallel to y, in which case A is a scalar. Therefore, vector division
>is not defined.
>
uniquely defined". Which, per se, is not a problem as long as the
limitations are understood.
We can (and do, under various occasions) use "pseudoinverses" in
linear algebra. These occur when using singular matrices. While, of
course, for a singular matrix A the inverse A^(-1) doesn't exist, one
can define pseudoinverse of A a matrix A^(~1) such that for every
vector fully in the "non null" subspace corresponding to A you've
A^(~1)*Av = v. such a pseudoinverse exists though, again, it is not
unique. No problem. In fact one can view the commonly used Green's
functions as just such pseudoinverses.
So, in a similar sense, division by a vector can be defined, though it
is not unique. And uniqueness can be provided by adding an additional
condition, for example taking as the multiplicative inverse of v the
shortest of all vectors such that v /dot v^(-1) = 1.
Mati Meron | "When you argue with a fool,
me...@cars.uchicago.edu | chances are he is doing just the same"
Phineas T Puddleduck
<mme...@cars3.uchicago.edu> wrote:
Yep the latter bit did add the disclaimer "not uniquely" but I thought
it was worth pushing his way ;-)
--
Relf's Law? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
"Bullshit repeated to the limit of infinity asymptotically approaches
the odour of roses."
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Jaffa cakes. Sweet delicious orangey jaffa goodness, and an abject lesson why
parroting information from the web will not teach you cosmology.
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Official emperor of sci.physics, head mumbler of the "Cult of INSANE SCIENCE".
Please pay no attention to my butt poking forward, it is expanding.
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
PWNER of Vert and TomGee since 2006
"I don't know that much math." - tomgee; 2 April 2006
"I don't claim to know what I'm talking about" - tomgee; 10 May 2006
PWNED
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
"Puddlefuck tou are on my kill file. Good bye" - Vert admits he cannot
calculate \gamma for a photon and admits defeat - 2nd July 2006
PWNED
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Ka-In Yen
Ka-In Yen wrote:
> Eric Gisse wrote:
> > and over while ignoring criticisms that would cause you to have to
> > abandon your work.
>
> Home work for Eric Gisse:
> A rectangle sits in 3D space. The area vector of the rectangle is A,
> and the legth vector of one side of the rectangle is L. Please find
> the length vector of the other side of the rectangle?
Dear Eric Gisse,
How long do you need to solve this problem? I am waiting
for your answer. You can discuss with Bilge and Puddleduck,
if the problem is difficult.
Phineas T Puddleduck
On 10/7/06 02:05, in article
1152493510.0...@p79g2000cwp.googlegroups.com, "Ka-In Yen"
<yen...@yahoo.com.tw> wrote:
> Dear Eric Gisse,
>
> How long do you need to solve this problem? I am waiting
> for your answer. You can discuss with Bilge and Puddleduck,
> if the problem is difficult.
Why should any of us waste our time with your BS?
--
Relf's Law? -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
"Bullshit repeated to the limit of infinity asymptotically approaches
the odour of roses."
Corollary -+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
łIt approaches the asymptote faster, the more Śpseduosą you throw in your
formulas.˛
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Jaffa cakes. Sweet delicious orange jaffa goodness, and an abject lesson
Why parroting information from the web will not teach you cosmology.
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Official emperor of sci.physics, head mumbler of the "Cult of INSANE
SCIENCE". Pay no attention to my butt poking forward, it is expanding.
-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
Bilge
The problem is that you are wrong. Since only you can correct
that problem, it will be impossile for anyone but you to solve.
Please continue waiting.
Ka-In Yen
Dear Eric Gisse,
You can run, but you can't hide.
Do you have any question to solve this problem?
Ka-In Yen
Sorcerer
"Ka-In Yen" <yen...@yahoo.com.tw> wrote in message
news:1156469606.5...@i42g2000cwa.googlegroups.com...
Goose will say it's moving at velocity v and divide by sqrt(1-v^2/c^2)
Androcles.
Sam Wormley
> A rectangle sits in 3D space. The area vector of the rectangle is A,
> and the legth vector of one side of the rectangle is L. Please find
> the length vector of the other side of the rectangle?
>
Too hard for Ka-In Yen? Hire tutor!