IIT JEE Advanced 2012 Paper 1

The point P is the intersection of the straight line joining the points Q (2, 3, 5) and R (1, –1, 4) with the plane 5x – 4y – z = 1. If S is the foot of the perpendicular drawn from the point T(2, 1, 4) to QR, then the length of the line segment PS is