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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))`

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

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The correct Answer is:
B
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