### Vectors Derivatives

given the vector $\vec{r}=r\hat{r}$ while $\hat{r}=\cos{wt}\hat{x}+\sin{wt}\hat{y}$ and $|r|=const$ compute:
a.$\frac{d\vec{r}}{dt}$.
b.$\frac{d}{dt}(\vec{r}\times \frac{d\vec{r}}{dt})$.