Find the area of a parallelogram whose adjacent sides are determined by the vectors $\overrightarrow{a}=\hat{i}-2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=2\hat{i}-6\hat{j}+3\hat{k}$.

If $\overline{a}=2\hat{i}-3\hat{j}+\hat{k}\text{ and }\overline{b}=3\hat{i}+\hat{j}+3\hat{k}$, then calculate $\overline{a}·\overline{b}$.

Find the angle between the vectors $\hat{i}-2\hat{j}+3\hat{k}\text{ and }3\hat{i}-2\hat{j}+\hat{k}$.

Find a unit vector perpendicular to the vectors $2\hat{i}-\hat{j}+\hat{k}\text{ and }3\hat{i}+4\hat{j}-\hat{k}$.