If $\overline{\mathrm{i}}-3\overline{\mathrm{j}}+\overline{\mathrm{k}}, 2\overline{\mathrm{i}}+4\overline{\mathrm{j}}-2\overline{\mathrm{k}}$ are sides of parallelogram then a unit vector parallel to one of a diagonals of the parallelogram is

$$\begin{gathered} \mathrm{Let} \overline{\mathrm{a}}=\hat{\mathrm{i}}-3\hat{\mathrm{j}}+\hat{\mathrm{k}}, \\ \overline{\mathrm{b}}=2\hat{\mathrm{i}}+4\hat{\mathrm{j}}-2\hat{k} \mathrm{represents} \mathrm{the} \mathrm{sides} \mathrm{of} \mathrm{the} \mathrm{parallelogram} \\ \overline{\mathrm{b}}+\overline{\mathrm{a}}=3\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \\ \overline{\mathrm{b}}-\overline{\mathrm{a}}=\widehat{ \mathrm{i}}+7\hat{\mathrm{j}}-\hat{\mathrm{k}} \mathrm{are} \mathrm{the} \mathrm{diagonals} \mathrm{of} \mathrm{the} \mathrm{parallelogram} \\ \mathrm{Unit} \mathrm{vector} \mathrm{parallel} \mathrm{to} \mathrm{the} \mathrm{diagonal} \mathrm{is}\frac{ \overline{\mathrm{b}}+\overline{\mathrm{a}}}{\left|\overline{\mathrm{b}}+\overline{\mathrm{a}}\right|}=\frac{3\hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}}{\sqrt{11}} \end{gathered}$$