For a, b ∈ Z and | a - b | ≤ 10, let the angle between the plane P: a x+y- z = b and the line l: x-1= a -y=z+1 be cos^-1(1/3). If the distance of the…

For $\displaystyle \mathrm{a}, \mathrm{b} \in \mathbb{Z}$ and $\displaystyle |\mathrm{a}-\mathrm{b}| \leq 10$, let the angle between the plane $\displaystyle \mathrm{P}: \mathrm{a} x+y-\mathrm{z}=\mathrm{b}$ and the line $\displaystyle l: x-1=\mathrm{a}-y=z+1$ be $\displaystyle \cos ^{-1}\left(\frac{1}{3}\right)$. If the distance of the point $\displaystyle (6,-6,4)$ from the plane $\displaystyle P$ is $\displaystyle 3 \sqrt{6}$, then $\displaystyle a^4+b^2$ is equal to