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JEE Main20236 Apr 2023Evening ShiftMathematicsThree Dimensional GeometryActual

A plane P contains the line of intersection of the plane r → · i ^ + j ^ + k ^ = 6 and r → · 2 i ^ + 3 j ^ + 4 k ^ = - 5 . If P passes through the point ( 0 , 2 , - 2 ) , then the square of distance of the point ( 12 , 12 , 18 ) from the plane P is

Options

  1. A620
  2. B155
  3. C310
  4. D1240

Correct answer

A. 620

Step-by-step solution

Given, A plane P contains the line of intersection of the plane r → · i ^ + j ^ + k ^ = 6 and r → · 2 i ^ + 3 j ^ + 4 k ^ = - 5 , Now let, P 1   :   x + y + z - 6 = 0 And P 2   :   2 x + 3 y + 4 z + 5 = 0 So, by family of planes concept we get, P   :   x + y + z - 6 + λ 2 x + 3 y + 4 z + 5 = 0 Also given plane P passes through ( 0 ,   2 ,   - 2 ) So, 0 + 2 - 2 - 6 + λ 4 + 6 - 8 + 5 = 0 ⇒ - 6 + λ 3 = 0 ⇒ λ = 2 Hence, equati

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