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JEE Main202228 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

Let the plane P : r → · a → = d contain the line of intersection of two planes r → · i ^ + 3 j ^ - k ^ = 6 and r → · - 6 i ^ + 5 j ^ - k ^ = 7 . If the plane P passes through the point 2 , 3 , 1 2 , then the value of 13 a → 2 d 2 is equal to

Options

  1. A90
  2. B93
  3. C95
  4. D97

Correct answer

B. 93

Step-by-step solution

Let the equation of plane passing through the line of intersection of planes P 1 : r → · i ^ + 3 j ^ - k ^ = 6 and P 2 : r → · - 6 i ^ + 5 j ^ - k ^ = 7 is P 1 + λ P 2 = 0 i.e. r → · i ^ + 3 j ^ - k ^ - 6 + λ r → · - 6 i ^ + 5 j ^ - k ^ - 7 = 0 ⇒ x + 3 y - z - 6 + λ - 6 x + 5 y - z - 7 = 0 Since it passes through the point 2 , 3 , 1 2 so 2 + 9 - 1 2 - 6 + λ - 12 + 15 - 1 2 - 7 = 0 ⇒ λ = 1 Hence, equation of plane is r → · -

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