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JEE Main202311 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let ( α , β , γ ) be the image of point P ( 2 , 3 , 5 ) in the plane 2 x + y - 3 z = 6 . Then α + β + γ is equal to

Options

  1. A5
  2. B10
  3. C12
  4. D9

Correct answer

B. 10

Step-by-step solution

Given plane is 2 x + y - 3 z = 6 . Since, α , β , γ is the image point of 2 , 3 , 5 in the given plane, so α - 2 2 = β - 3 1 = γ - 5 - 3 = - 2 4 + 3 - 15 - 6 4 + 1 + 9 ⇒ α - 2 2 = β - 3 1 = γ - 5 - 3 = 2 ⇒ α - 2 2 = 2 ;   β - 3 1 = 2 ;   γ - 5 - 3 = 2 ∴ α = 6 ,   β = 5 ,   γ = - 1 Hence, α + β + γ = 6 + 5 - 1 = 10 Hence this is the required option.

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