Chapter 13.2, Problem 38E

To determine

To show that $\Vert r\left(t\right)\Vert$ is constant and conclude that $r\left(t\right)$ and $r^{\prime }\left(t\right)$ are orthogonal for $r\left(t\right)=\langle 3\cos t,5\sin t,4\cos t\rangle$. Also, verify that $r\left(t\right)$ and $r^{\prime }\left(t\right)$ are orthogonal by computing $r^{\prime }\left(t\right)$.