Mobius strip computing unit normal field at 2 points

[joeyjokester]

Homework Statement

I am given this parametrization of the mobius band:
F(s,t) = (cos(t)+s*cos(t)*cos(t/2), sin(t)+s*sin(t)*cos(t/2), s*sin(t/2))
Let F1 be F restricted to (0,2*pi) X (-1,1).
Let F2 be F restricted to (-pi,pi) X (-1,1).
let N1 be the unit normal field determined by F1
let N2 be the unit normal field determined by F2

The question reads:
Compute the unit normal field for N1, N2 at the points (0,1,0) and (0,-1,0).

Homework Equations

N(t) = (dF/ds X dF/dt)/ ||dF/ds X dF/dt||

The Attempt at a Solution

I am unsure how to begin on this. I am looking for a starting block. Obviously I want to plug in the point before taking cross products? How do I do this when F(s,t) takes 2 parameters, but I am given a point of the form (x,y,z). This is troublesome. I have computed the partials dF/ds and dF/dt, but I don't know what to do with them.. I don't want to take this nasty cross product.

thanks

 

[lanedance]

take the derivatives to find the tangent vectors aligned with each parameter

then substitute in the given values & calculate the cross products, shoudln;t be too messy after substitution

 

[joeyjokester]

That is exactly my question. How do I substitute in the given values?

 

[lanedance]

you'll need to determine s & t for the given points first, to do that consider what would lead to the terms being zero