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** Q 1688167907. ** 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

**JEE 2012 ADVANCED Paper - 1**