Practice Problems

1. Resolve a vector of magnitude 10 at $30^\circ$
2. Find unit vector of $\vec{A} = 2\hat{i} + 3\hat{j} + 6\hat{k}$
3. Compute $\vec{A} \cdot \vec{B}$
4. Compute $\vec{A} \times \vec{B}$
5. Find dimensions of energy
6. Prove dot product is commutative
7. Show cross product is not commutative
8. A particle moves as $\vec{r} = t^2 \hat{i} + 2t \hat{j}$. Find velocity