Let $\overline{a}=\alpha \overline{i}+2\overline{j}-\overline{k}$ and $\overline{b}=-2\overline{i}+\alpha \overline{j}+\overline{k}$ where $\alpha \in R$. If the area of the parallelogram whose adjacent sides are represented by the vectors $\overline{a}$and $\overline{b}$ is $\sqrt{15({\alpha }^2+4)}$ then the value of  $2{\left|\overline{a}\right|}^2+(\overline{a}.\overline{b}){\left|\overline{b}\right|}^2$