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JEE Main20208 Jan 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The mirror image of the point 1 , 2 , 3 , in a plane is - 7 3 , - 4 3 , - 1 3 . Which of the following points lies on this plane?

Options

  1. A1 ,   1 ,   1
  2. B1 , - 1 ,   1
  3. C- 1 , - 1 ,   1
  4. D- 1 , - 1 , - 1

Correct answer

B. 1 , - 1 ,   1

Step-by-step solution

Assume, Q be the midpoint of 1 , 2 , 3 & - 7 3 , - 4 3 , - 1 3 So, coordinate of Q = 1 - 7 3 2 , 2 - 4 3 2 , 3 - 1 3 2 = - 2 3 , 1 3 , 4 3 The direction ratio of normal to the plane is 1 + 7 3 ,   2 + 4 3 ,   3 + 1 3 = 10 3 , 10 3 , 10 3   ⇒ 1 , 1 , 1 So, equation of plane is x + y + z = 1 . So, 1 , - 1 , 1 lies on this plane.

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