Normal vectors for vector-valued functions

[Sean Fitzpatrick]

Something I noticed this week: for vector valued functions, we define the unit normal vector as the derivative of the unit tangent vector, normalized.

This is mostly fine, with one catch: for a straight line, the unit tangent vector is constant, so the unit normal is not defined in this case.

Should there be an aside that points this out? And in the case of a line, do we just say that there is no preferred choice of normal vector?

[gregory...@gmail.com]

Ha! Nice catch.

Yes, an aside should address this. And I can't back this up as `right', but I feel that the preferred choice is a counter-clockwise rotation of T.

So if T = < a, b>, then N = < -b, a>.

[Sean Fitzpatrick]

Right, but then what do we do with the line

<x,y,z>=p_0+t<a,b,c>? :-)

[Sean Fitzpatrick]

I've added an aside to address this. I think the "updates and edits" pull request is ready for review.

I'm about to start building HTML. Need to do images first, since we updated some and added new ones.