In `R^3`, let L be a straight line passing through the origin. Suppose that all the points on `L` are at a constant dist

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Q 1658167904.     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`?
JEE 2015 ADVANCED Paper 1

(This question may have multiple correct answers)

A ` (0, - frac {5}{6}, - frac {2}{3 })`
B `(- frac {1}{6}, - frac {1}{3}, frac {1}{6} )`
C `(- frac {5}{6}, 0, frac {1}{6} )`
D `(- frac {1}{3}, 0, frac {2}{3} )`

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Solution
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)

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