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JEE Main202311 Apr 2023Morning ShiftMathematicsThree Dimensional GeometryActual

If the equation of the plane that contains the point ( - 2 , 3 , 5 ) and is perpendicular to each of the planes 2 x + 4 y + 5 z = 8 and 3 x - 2 y + 3 z = 5 is α x + β y + γ z + 97 = 0 then α + β + γ =

Options

  1. A15
  2. B18
  3. C16
  4. D17

Correct answer

A. 15

Step-by-step solution

Given The equation of the plane that contains the point - 2 , 3 , 5 and is perpendicular to each of the planes 2 x + 4 y + 5 z = 8 and 3 x - 2 y + 3 z = 5 is α x + β y + γ z + 97 = 0 Now satisfying the point - 2 , 3 , 5 in plane P : α x + β y + γ z + 97 = 0 we get, - 2 α + 3 β + 5 γ + 97 = 0     . . . . . . . . i And using perpendicular condition 2 x + 4 y + 5 z = 8 and α x + β y + γ z + 97 = 0 we get, 2 α + 4 β + 5 γ = 0   .

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