Chapter 12.2, Problem 42E

(a)

To determine

To calculate: The expression $\frac{d}{dt}\left[r\left(t\right)\cdot u\left(t\right)\right]$ for the functions $r\left(t\right)=\cos ti+\sin tj+tk\text{ and }u\left(t\right)=j+tk$.

(b)

To determine

To calculate: The expression $\frac{d}{dt}\left[r\left(t\right)\times u\left(t\right)\right]$ for the provided vectors $r\left(t\right)=\cos ti+\sin tj+tk\text{ and }u\left(t\right)=j+tk$.