Upgrade subject to access all content

Which of the following statements is not always true for the vector-valued functions ${\bf r}(t)$ and ${\bf s}(t)$?

The expression ${\bf r''}(t) \cdot {\bf r'}(t) $ is not a vector-valued function.

If ${\bf r}(t) \cdot {\bf r}(t)$ is a constant function, then ${\bf r}(t) \cdot {\bf r'}(t) =0$ for all $t$.

If ${\bf r}(t) \cdot {\bf r'}(t) =0$ for all $t$, then ${\bf r}(t) \cdot {\bf r}(t)$ is a constant function.

The identity $||{\bf r}(t)\cdot {\bf s}(t)||= ||{\bf r}(t)||||{\bf s}(t)||$ holds for all $t$.

The identity ${\bf r}(t) \times {\bf r'}(t)=0$ holds for all $t$.