For \(a, b \in Z\) and \(|a-b| \leq 10\), let the angle between the plane \(P: a x+y-z=b\) and the line \(l: x-1=a-y=z+1…

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

[JEE Main 2023, 8 Apr (Shift 2)]