1.If $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$, find the angle between $\vec{A}$ and $\vec{B}$.
2.Find a unit vector perpendicular to both $\vec{A} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{B} = \hat{i} - \hat{j} + 2\hat{k}$.
3.Find the area of a parallelogram whose adjacent sides are $\vec{A} = 3\hat{i} + \hat{j} + 4\hat{k}$ and $\vec{B} = \hat{i} - \hat{j} + \hat{k}$.
4.A vector $\vec{A}$ makes angles $\alpha, \beta, \gamma$ with x, y, z axes. Prove that $\cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1$.
5.Find the position vector of a particle at time $t$ if velocity $\vec{v}(t) = (2t\hat{i} + 3t^2\hat{j})\text{ m/s}$ and $\vec{r}(0) = \hat{i}$.
