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JEE Main202126 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be the plane passing through the point ( 1 , 2 , 3 ) and the line of intersection of the planes r → · ( i ^ + j ^ + 4 k ^ ) = 16 & r → · ( - i ^ + j ^ + k ^ ) = 6 . Then which of the following points does NOT lie on P ?

Options

  1. A4 , 2 , 2
  2. B6 , - 6 , 2
  3. C- 8 , 8 , 6
  4. D3 , 3 , 2

Correct answer

A. 4 , 2 , 2

Step-by-step solution

x + y + 4 z - 16 + λ - x + y + z - 6 = 0 Passes through 1 , 2 , 3 - 1 + λ - 2 = 0 λ = - 1 2 2 x + y + 4 z - 16 - - x + y + z - 6 = 0 3 x + y + 7 z - 26 = 0 Now put points given in option and then we get 4 , 2 , 2 as required answer.

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