(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

DoCarmo Section 1.5 problem 1 part d. Show that the lines containing n(s) and passing through a(s) [a is the curve, and n(s) is the unit normal vector] meet the z axis under a constant angle of pi/2.

Helix: a(s) = (a cos(s/c_, a sin(s/c), b*s/c), so I computed n(s) = (cos(s/c),sin(s/c),0).

2. Relevant equations

3. The attempt at a solution

I think the principal normal containing n(s) and a(s) is : L(t) = (t-s)*n(s) + a(s). THis is because L'(t) = n(s), and L(s) = a(s), but when I try to show d/dt ( L(t) . z/Norm(L(t))) = Cos(theta) =0, I keep getting that it is not zero, due to the z-component of a(s), and the norm of L(t), which I compute to be ((Norm a)^2+(t-s)^2)^0.5, by orthogonality of n(s) and a(s).

Is there something I am donig wrong?

Thanks,

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# Homework Help: Principal normal line to helix is normal to z axis

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