Let $\overline{\mathrm{a}}={\mathrm{a}}_1\overline{\mathrm{i}}+{\mathrm{a}}_2\overline{\mathrm{j}}+{\mathrm{a}}_3\overline{\mathrm{k}}, \overline{\mathrm{b}}={\mathrm{b}}_1\overline{\mathrm{i}}+{\mathrm{b}}_2\overline{\mathrm{j}}+{\mathrm{b}}_3\overline{\mathrm{k}}, \overline{\mathrm{c}}={\mathrm{c}}_1\overline{\mathrm{i}}+{\mathrm{c}}_2\overline{\mathrm{j}}+{\mathrm{c}}_3\overline{\mathrm{k}}$ be three non-zero vectors such that $\overline{\mathrm{c} }$is a unit vector perpendecular to both $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ .

If the angle between $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$ is $\mathrm{\pi }/ 6$ then ${\left|\begin{array}{ccc}{\mathrm{a}}_1& {\mathrm{a}}_2& {\mathrm{a}}_3\\ {\mathrm{b}}_1& {\mathrm{b}}_2& {\mathrm{b}}_3\\ {\mathrm{c}}_1& {\mathrm{c}}_2& {\mathrm{c}}_3\end{array}\right|}^2=$