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JEE Main202127 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane passing through the line of intersection of the planes r → · ( i ^ + j ^ + k ^ ) = 1 and r → · ( 2 i ^ + 3 j ^ - k ^ ) + 4 = 0 and parallel to the x -axis, is

Options

  1. Ar → · ( i ^ + 3 k ^ ) + 6 = 0
  2. Br → · ( i ^ - 3 k ^ ) + 6 = 0
  3. Cr → · ( j ^ - 3 k ^ ) - 6 = 0
  4. Dr → · ( j ^ - 3 k ^ ) + 6 = 0

Correct answer

D. r → · ( j ^ - 3 k ^ ) + 6 = 0

Step-by-step solution

P 1 : r → · ( i ^ + j ^ + k ^ ) = 1 ⇒ x + y + z - 1 = 0 P 2 :   r → · ( 2 i ^ + 3 j ^ - k ^ ) + 4 = 0 ⇒ 2 x + 3 y - z + 4 = 0 The equation of the plane passing through the line of intersection of the planes: P 1 + λ P 2 = 0 ( 1 + 2 λ ) x + ( 1 + 3 λ ) y + ( 1 - λ ) z = 1 - 4 λ . . . i Parallel to x - axis a 1 a 2 + b 1 b 2 + c 1 c 2 = 0 ( 1 + 2 λ ) 1 + ( 1 + 3 λ ) 0 + ( 1 − λ ) 0 = 0 λ = − 1 2 1 − 3 2 y + 1 + 1 2 z

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