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JEE Main202228 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

If two distinct point Q , R lie on the line of intersection of the planes - x + 2 y - z = 0 and 3 x - 5 y + 2 z = 0 and P Q = P R = 18 where the point P is 1 , - 2 , 3 , then the area of the triangle P Q R is equal to

Options

  1. A2 3 38
  2. B4 3 38
  3. C8 3 38
  4. D152 3

Correct answer

B. 4 3 38

Step-by-step solution

Given equations of plane are - x + 2 y - z = 0 and 3 x - 5 y + 2 z = 0 Now a vector perpendicular to both the planes is given by n → = i ^ j ^ k ^ - 1 2 - 1 3 - 5 2 = i ^ - 1 - j ^ 1 + k ^ - 1 n → = - i ^ - j ^ - k ^ For a point on the line of intersection of both the planes let z = 0 , so x = 2 y   &   8 x = 5 y i.e. a point on the line will be 0 , 0 , 0 So equation of line of intersection of both these planes will be x 1 = y 1 = z 1 The DR's of Q R are 1 ,   1 ,   1 Let the

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