JEE Main 2022 Mathematics question

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line , R. Then, which of the following points lies on T?

(1)(2, 1, 0)
(2)(1, 2, 1)Correct
(3)(1, 2, 2)
(4)(1, 3, 2)

Answer: (2)

Solution

The image of P(1, 2, 1) in x + 2y + 2z = 16: (x − 1)/1 = (y − 2)/2 = (z − 1)/2 = −2(1 + 4 + 2 − 16)/9 = 2, so Q = (3, 6, 5). The plane T contains the point A(0, 0, −1) and the direction (1, 1,

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Question ID VK-035239