JEE Advanced | 2015Straight LineHard
Question
In 
, let L be a straight line passing through the origin. Suppose that all the points on L are at aconstant distance from the two planes P1 : x + 2y − z + 1 = 0 and P2 : 2x − y + z − 1 = 0. Let Mbe the locus of the feet of the perpendiculars drawn from the points on L to the plane P1. Which ofthe following points lie(s) on M ?
, let L be a straight line passing through the origin. Suppose that all the points on L are at aconstant distance from the two planes P1 : x + 2y − z + 1 = 0 and P2 : 2x − y + z − 1 = 0. Let Mbe the locus of the feet of the perpendiculars drawn from the points on L to the plane P1. Which ofthe following points lie(s) on M ?Options
A.
B.
C.
D.
Solution
Straight line ′L′ is parallel to line of intersection of plane P1 & plane P2.
∴ Equation of line ′L′ is
......(1)
satisfying in plane P1
k + λ + 4k - 6λ + k + 5λ + 1 = 0
6k = - 1
putting in (1) required locus is
x = -
+ λ
y = -
- 3λ
z =
- 3λ
Now check the options.
∴ Equation of line ′L′ is
......(1)satisfying in plane P1
k + λ + 4k - 6λ + k + 5λ + 1 = 0
6k = - 1
putting in (1) required locus is
x = -
+ λy = -
- 3λz =
- 3λNow check the options.
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