Let the plane P: r · a =d contain the line of intersection of two planes r ·( i +3 j - k )=6 and r ·(-6 i +5 j - k )=7. If the plane P passes through…

Let the plane $\displaystyle P: \vec{r} \cdot \vec{a}=d$ contain the line of intersection of two planes $\displaystyle \vec{r} \cdot(\hat{i}+3 \hat{j}-\hat{k})=6$ and $\displaystyle \vec{r} \cdot(-6 \hat{i}+5 \hat{j}-\hat{k})=7$. If the plane $\displaystyle P$ passes through the point $\displaystyle \left(2,3, \frac{1}{2}\right)$, then the value of $\displaystyle \frac{|13 \vec{a}|^2}{d^2}$ is equal to