Chapter 12.2, Problem 42ES

Determine whether the statement is true or false. Explain your answer.

If $\text{r}\left(t\right)$ is a vector-valued function in 2-space and $‖\text{r}\left(t\right)‖$ is constant, then $\text{r}\left(t\right)$ and $\text{<msup> r <mo> ′ </mo> </msup>}\left(t\right)$ are parallel vectors for all t.