Let the plane \(P: 4 x-y+z=10\) be rotated by an angle \(\pi / 2\) about its line of intersection with the plane \(x+y-z…

Let the plane \(P: 4 x-y+z=10\) be rotated by an angle \(\pi / 2\) about its line of intersection with the plane \(x+y-z=4\). If \(\alpha\) is the distance of the point \((2,3,-4)\) from the new position of the plane \(P\), then \(35 \alpha\) is

[JEE Main 2023, 12 Apr (Shift 1)]