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