1.Show that $\nabla \times (\nabla \times \vec{A}) = \nabla(\nabla \cdot \vec{A}) - \nabla^2 \vec{A}$.
2.Evaluate $\oint_C \vec{F} \cdot d\vec{r}$ where $\vec{F} = (x - y)\hat{i} + (x + y)\hat{j}$ around the unit circle $C$ using Green's Theorem.
3.Prove that if $\vec{F}$ is a conservative force field ($\nabla \times \vec{F} = 0$), then $\vec{F} = -\nabla U$ for some scalar potential function $U$.
