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JEE Main202131 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Let the equation of the plane, that passes through the point ( 1 , 4 , - 3 ) and contains the line of intersection of the planes 3 x - 2 y + 4 z - 7 = 0 and x + 5 y - 2 z + 9 = 0 , be α x + β y + γ z + 3 = 0 , then α + β + γ is equal to :

Options

  1. A- 15
  2. B15
  3. C- 23
  4. D23

Correct answer

C. - 23

Step-by-step solution

Given plane equations are 3 x - 2 y + 4 z - 7   =   0   &   x + 5 y - 2 z + 9 = 0 Family of planes ⇒ P 1 + λ P 2 = 0 ⇒    ( 3 x - 2 y + 4 z - 7 ) + λ ( x + 5 y - 2 z + 9 ) = 0 Passing through the point ( 1 , 4 , - 3 ) ⇒    ( 3 - 8 - 12 - 7 ) + λ ( 1 + 20 + 6 + 9 ) = 0 ⇒    λ = 24 36 = 2 3 Required equation of plane is 3 + 2 3 x + y - 2 + 10 3 + z 4 - 4 3 - 7 + 6 = 0 ⇒    - 11 x - 4 y - 8 z + 3 = 0 Given

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