JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 17

Let the plane $P:\vec r\cdot\vec a=d$ contain the line of intersection of two planes $\vec r\cdot\left(\hat i+3\hat j-\hat k\right)=6$ and $\vec r\cdot\left(-6\hat i+5\hat j-\hat k\right)=7$. If the plane P passes through the point $\left(2,3,\dfrac12\right)$, then the value of $\dfrac{\left|13\vec a\right|^2}{d^2}$ is equal to