3d Geometry

Let the plane P: \(4 x-y+z=10\) be rotated by an angle \(\frac{\pi}{2}\) 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 \(\mathrm{P}\), then \(35 \alpha\) is equal to :