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In R^3, let L be a straight line passing...

In `R^3`, let L be a straight line passing throughthe origin. Suppose that all 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 t the plane `P_1`. Which of the following point(s) 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)`

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