Chapter 12.5, Problem 2QCE

Let $\text{r}\left(t\right)$ be a smooth vector-valued function with curvature $\kappa \left(t\right).$

(a) The curvature may be expressed in terms of $\text{<msup> T <mo> ′ </mo> </msup>}\left(t\right)\text{ and <msup> r <mo> ′ </mo> </msup>}\left(t\right)\text{ as }\kappa \left(t\right)=\text{\_\_\_\_\_\_\_\_}\text{.}$

(b) The curvature may be expressed directly in terms of $\text{<msup> r <mo> ′ </mo> </msup>}\left(t\right)\text{ and <msup> r <mo> ″ </mo> </msup>}\left(t\right)\text{ as }\kappa \left(t\right)=\text{\_\_\_\_\_\_\_\_}\text{.}$