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In R^(3), let L be a straight line passi...

In `R^(3)`, let L be a straight line passing through the origin. Suppose that all the points on L are at a constant distance from the two planes `P_(1) : x + 2y -z + 1 = 0 and P_(2) : 2x -y + z -1 = 0`. Let M be the locus of the feet of the perpendiculars drawn from the points on L to the plane `P_(1)`. Which of the following points lie (s) on M ?

A

`(0, -(5)/(6), (2)/(3))`

B

`(-(1)/(6), (1)/(3), (1)/(6))`

C

`(-(5)/(6), 0, (1)/(6))`

D

`(-(1)/(3), 0, (2)/(3))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
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