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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:

A

`(1)/(sqrt2)`

B

`sqrt2`

C

2

D

`2sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
a

Direction ratios of QR are 1, 4, 1 ltBrgt Coordinate of `P-= ((4)/(3),(1)/(3), (13)/(3))`
Direction ratios of `PT` are 2, 2, -1
Angle between `QR and PT` is `45^(@)`
And `PT =1`
`rArr" "PS=TS= (1)/(sqrt2)`
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