(a) (3 marks) Show that if r(t) is a smooth vector function with ||r(t)|| = 1, then (d)/(dt)r(t)

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(a) (3 marks) Show that if \overrightarrow{r}(t) is a smooth vector function with $||\overrightarrow{r}(t)|| = 1$, then \frac{d}{dt}\overrightarrow{r}(t) \cdot \overrightarrow{r}(t) = 0.