ABCD is a quadrilateral with $\overline{\mathrm{AB}}=\overline{\mathrm{a}}, \overline{\mathrm{AD}}=\overline{\mathrm{b}}$ and $\overline{\mathrm{AC}}=2 \overline{\mathrm{a}}+3 \overline{\mathrm{~b}}$. If its area is $\alpha$ times the area of the parallelogram with $\mathrm{AB}, \mathrm{AD}$ as adjacent sides, then the value of $\alpha$ is

If $\overline{\mathrm{c}}=5 \overline{\mathrm{a}}+6 \overline{\mathrm{~b}}$ and $3 \overline{\mathrm{c}}=\overline{\mathrm{a}}-4 \overline{\mathrm{~b}}$ then

If $\overline{\mathrm{a}}=\frac{1}{\sqrt{10}}(3 \hat{\mathrm{i}}+\hat{\mathrm{k}}), \overline{\mathrm{b}}=\frac{1}{7}(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-6 \hat{\mathrm{k}})$, then the value of $(\overline{\mathrm{a}}-2 \overline{\mathrm{~b}}) \cdot\{(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times(2 \overline{\mathrm{a}}+\overline{\mathrm{b}})\}$ is