Chapter 14.4, Problem 88E

To determine

To prove:

$\frac{dN}{ds}=-kT+\tau B$ using the following steps:

(a) Show that $\frac{dN}{ds}$ is orthogonal toN. Also, conclude that $\frac{dN}{ds}$ lies in the plane spanned by T and B, and hence, $\frac{dN}{ds}=aT+bB$ for some scalars a, b.

(b) Show that $T\cdot \frac{dN}{ds}=-N\cdot \frac{dT}{ds}$ using $N\cdot T=0$ and compute a andb.