I have no idea about vector calculus, rather i am comfortable with abstract algebra. One of my juniors asked the following questions:
(1) Prove that $\nabla(\frac{x}{r^2})=\frac{-2x}{r^4}$, where $\nabla$ is gradient operator.
(2) Solve $\int a.(r\times \frac{d^2r}{dt^2})dt$.
I regret, if the question is not suitable for this forum.