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JEE Main202229 Jun 2022Evening ShiftMathematicsThree Dimensional GeometryActual

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

Options

  1. A2 ,   1 ,   0
  2. B1 ,   2 ,   1
  3. C1 ,   2 ,   2
  4. D1 ,   3 ,   2

Correct answer

B. 1 ,   2 ,   1

Step-by-step solution

We know that by image formula, image of P 1 ,   2 ,   1 in x + 2 y + 2 z - 16 = 0 is given by Q 4 ,   8 ,   7 Now equation of plane will be given by T = x - x 1 y - y 1 z - z 1 a 1 b 1 c 1 a 2 b 2 c 2 = 0 ⇒ T = x - 0 y - 0 z + 1 4 - 0 8 - 0 7 + 1 1 1 2 = 0 ⇒ 2 x - z = 1 Now from options, only point B 1 ,   2 ,   1 lies on it.

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