3D Geometry 3 Question 52
52. In , let be a straight line passing through the origin. Suppose that all the points on are at a constant distance from the two planes and . Let be the locus of the foot of the perpendiculars drawn from the points on to the plane . Which of the following point(s) lie(s) on ?
(2015 Adv.)
(a)
(b)
(c)
(d)
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Answer:
Correct Answer: 52. (b, d)
Solution:
- Since,
is at constant distance from two planes and . Therefore, is parallel to the line through intersection of and .
Now, equation of
For any point on
[say]
i.e.
If
which satisfy options (a) and (b).