Chapter 16.5, Problem 31E

Let $r=xi+yj+zk$ and $r=\left|r\right|$.

Verify each identity.

(a) $\nabla r=r/r$

(b) $\nabla \times r=0$

(c) $\nabla \left(1/r\right)=-r/r^3$

(d) $\nabla \ln r=r/r^2$