Question

The sides of parallelogam are $2\hat{i}+4\hat{j}-5\hat{k}$ and $\hat{i}+2\hat{j}+3\hat{k}$. Find the unit vectors parallel to the diagonals.

Answer 1

Diagonal$=\overrightarrow{a}+\overrightarrow{b}=3\hat{i}+6\hat{j}-2\hat{k}$

Unit vector$=\frac{3\hat{i}+6\hat{j}-2\hat{k}}{\sqrt{49}}=$$\frac{3\hat{i}+6\hat{j}-2\hat{k}}{7}$