If $\displaystyle \underline{A} = f(r)\underline{r}$ , use spherical polar coordinates to find $\displaystyle f(r)$ if

(i) $\displaystyle \underline{\nabla} \cdot \underline{A} = 0 $ and

(ii) $\displaystyle \underline{\nabla} \times \underline{A} = 0 $

Not sure how to do the above I think I manged to find

$\displaystyle f(r) = \frac{C}{r^3}$ , but I don't know what to do next...