JEE Advanced 2012 Paper 1 Mathematics Q9

Mathematics

Problem

The point PP is the intersection of the straight line joining the points Q(2,3,5)Q(2,3,5) and R(1,−1,4)R(1,-1,4) with the plane 5x−4y−z=15x-4y-z=1. If SS is the foot of the perpendicular drawn from the point T(2,1,4)T(2,1,4) to QRQR, then the length of the line segment PSPS is

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