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JEE Main202310 Apr 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let the image of the point P ( 1 , 2 , 6 ) in the plane passing through the points A ( 1 , 2 , 0 ) and B ( 1 , 4 , 1 ) C ( 0 , 5 , 1 ) be Q ( α , β , γ ) . Then α 2 + β 2 + γ 2 equal to

Options

  1. A65
  2. B62
  3. C76
  4. D70

Correct answer

A. 65

Step-by-step solution

Plane passes through the points A ( 1 ,   2 ,   0 ) , B ( 1 ,   4 ,   1 ) and C ( 0 ,   5 ,   1 ) We know that the equation of a plane passing through three non-collinear points x 1 , y 1 , z 1 , x 2 , y 2 , z 2 , x 3 , y 3 , z 3 is x - x 1 y - y 1 z - z 1 x 2 - x 1 y 2 - y 1 z 2 - z 1 x 3 - x 1 y 3 - y 1 z 3 - z 1 = 0 ⇒ x - 1 y - 2 z - 0 1 - 1 4 - 2 1 - 0 0 - 1 5 - 2 1 - 0 = 0 ⇒ x - 1 y - 2 z - 0 0 2 1 - 1 3 1 = x - 1 2 - 3 - y - 2 0 + 1 + z 0 + 2 = 0 ⇒ - x + 1 - y +

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