Find the divergence and curl of the vector field $\bf F$$=r^5\bf a$$+2r^3(\bf a\cdot r)r$, where $\bf a$ is a constant vector and $r=|\bf r|$.
My thought was to let $\bf r$$=(r_1,r_2,\cdots r_n)$, so that $r=(r_1^2+\cdots +r_n^2)^{\frac{1}{2}}$ and $\bf a$$=(a_1,\cdots a_n)$. But with this method I'm not sure at all how to find the required result. Any tips?