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In R^(2), L be a straight line passing t...

In `R^(2),` 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:
B
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