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

Suppose that r(s) defines a curve parametrically with respect to arc length and the r′(s) is nonzero on the curve. Show that dB/ds is orthogonal to both

B(s) and T(s). Conclude that there is a scalar function τ(s) such that

dB/ds = −τ (s)N . (This function τ is known as the torsion of the curve.)

3. The attempt at a solution

Not really sure how to approach this one. I'd say we need to show some way that dB/ds x B = 0 and the same with T, but I'm not sure how to do it completely algebraically... As for τ, is it enough just to show that dB/ds is parallel to N? This would simply follow from the proof that it is orthogonal to B and T, since T x B = N (or T x N = B)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Orthogonal derivative of binormal vector.

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**