# Curvilinear Coordinates and Vector Calculus

## Homework Statement

With $\vec{L}$ = -i$\vec{r}$ x $\nabla$, verify the operator identities

$\nabla = \hat{r}\frac{\partial }{\partial \vec{r}}-i\frac{\vec{r}\times\vec{L}}{r^{2}}$
and
$\vec{r} \bigtriangledown ^2 - \bigtriangledown (1+\vec{r}\frac{\partial }{\partial \vec{r}})=i\bigtriangledown \times \vec{L}$

## The Attempt at a Solution

... I tried to expand it, and use some identities... But the equation becomes super complicated... Help!

$$\vec{A}\times \left(\vec{B}\times\vec{C}\right) = \ ...$$