vectors to create an orthonogal base

[Johan Lans]

Hi, I'm having this problem:
I have three vectors with blanks, v=(0.8, -0.6, []), u=([],[],1),
w=([],0.8,[]). I'm supposed to fill in the blanks so that the vectors
create an orthonogal base.
Would be thankful for tips and clues rather than a straight answer.

Thanks/ Johan

[Arturo Magidin]

In article <d64de$454f68ce$50d8bcf9$27...@news.chello.se>,

Johan Lans <nos...@nospam.com> wrote:
>Hi, I'm having this problem:
>I have three vectors with blanks, v=(0.8, -0.6, []), u=([],[],1),
>w=([],0.8,[]). I'm supposed to fill in the blanks so that the vectors
>create an orthonogal base.

I assume you mean "orthogonal". I fixed the subject as well.

With respect to what inner product?

> Would be thankful for tips and clues rather than a straight answer.

I assume the usual (dot) product.

Write

v = (0.8, -0.6, a)
u = (b, c, 1)
w = (d, 0.8, e).

Since <u,v>=0, we have

0 = <(0.8,-0.6,a),(b,c,1)>
= a + 0.8 b - 0.6c

From <u,w>=0, you get

0 = bd + 0.8 c + e

and from <v,w>=0 you get

0 = 0.8d +ae - 0.48

Try solving for a, b, c, d, and e.

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================

Arturo Magidin
magidin-at-member-ams-org

[kilian heckrodt]

orthogonal means the dot product of the vectors is 0.
so v.u=0, v.w=0,u.w=0.
Applying the definition of the dot product, you will get 3 linear
equations with 3 unknowns, which you solve via gauss elimination or
some other method

[Johan Lans]

Ok, thanks both, I solved it.

/Johan