Vector Algebra

If $\bar{a}, \bar{b}, \bar{c}$ are three vectors such that $|\overrightarrow{\mathrm{a}}|=\sqrt{31}, 4|\overrightarrow{\mathrm{~b}}|=|\overrightarrow{\mathrm{c}}|=2$ and $2(\overline{\mathrm{a}} \times \overline{\mathrm{b}})=3(\overline{\mathrm{c}} \times \overline{\mathrm{a}})$ and if the angle between $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ is $\frac{2 \pi}{3}$ then $\left|\frac{\bar{a} \times \bar{c}}{\bar{a} \cdot \bar{b}}\right|^2=$