Chapter 12, Problem 30RE

(a) What does Theorem 12.2.8 tell you about the velocity vector of a particle that moves over a sphere?

(b) What does Theorem 12.2.8 tell you about the acceleration vector of a particle that moves with constant speed?

(c) Show that the particle with position function $\text{r}\left(t\right)=\sqrt{1-\frac{1}{4}{\cos }^{2}t}\cos t\text{i}+\sqrt{1-\frac{1}{4}{\cos }^{2}t}\sin t\text{j}+\frac{1}{2}\cos t\text{k}$ moves over a sphere.