1.Prove the vector triple product expansion formula $\vec{A} \times (\vec{B} \times \vec{C}) = (\vec{A} \cdot \vec{C})\vec{B} - (\vec{A} \cdot \vec{B})\vec{C}$.
2.Find the volume of a parallelepiped formed by vectors $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$, $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$, $\vec{c} = 3\hat{i} - \hat{j} + 2\hat{k}$.
3.If $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ and $r = |\vec{r}|$, calculate $\nabla r^n$.
4.Find the work done by a force field $\vec{F} = x^2\hat{i} - xy\hat{j}$ along the straight line from $(0,0)$ to $(1,1)$.
