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