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The point P is the intersection of the s...

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:

Text Solution

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`L:(x-1)/1=(y+1)/4=(z-4)/1=lambda`
`(lambda+1,4lambda-1,lambda+4)`
`5x-4y-z=1`
`5(lambda+1)-4(4lambda-1)-(lambda+4)=1`
`-12lambda+5=1`
`lambda=1/3`
`vec(TS)(lambda-1,4lambda-2,lambda)`
`(1,4,1)`
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