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JEE Main202126 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

A plane P contains the line x + 2 y + 3 z + 1 = 0 = x - y - z - 6 , and is perpendicular to the plane - 2 x + y + z + 8 = 0 . Then which of the following points lies on P ?

Options

  1. A( 2 , - 1 , 1 )
  2. B( 0 , 1 , 1 )
  3. C( - 1 , 1 , 2 )
  4. D( 1 , 0 , 1 )

Correct answer

B. ( 0 , 1 , 1 )

Step-by-step solution

A plane which containing the line x + 2 y + 3 z + 1 = 0 = x - y - z - 6 is x + 2 y + 3 z + 1 + λ x - y - z - 6 = 0 ⇒ ( 1 + λ ) x + ( 2 - λ ) y + ( 3 - λ ) z + 1 - 6 λ = 0 This plane is perpendicular to the plane - 2 x + y + z + 8 = 0 then - 2 ( 1 + λ ) + 1 ( 2 - λ ) + 1 ( 3 - λ ) = 0 ⇒ λ = 3 4 Equation of plane is 7 4 x + 5 4 y + 9 4 z = 14 4 ⇒ 7 x + 5 y + 9 z = 14 Clearly, ( 0 , 1 , 1 ) lies on the plane.

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