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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the lines x 1 = y - 1 - 1 = z + 2 2 , x 2 = y - 1 1 = z + 2 1 , x - 1 = y - 1 - 1 = z + 2 1 intersect the plane x + y - z = 0 at P , Q , R respectively, then the area (in sq. units) of triangle P Q R is

Options

  1. A3
  2. B4 7 3
  3. C9 8 3
  4. D9 4 3

Correct answer

C. 9 8 3

Step-by-step solution

Coordinates of P , Q , R are r 1 , - r 1 + 1 , 2 r 1 - 2 , 2 r 2 , r 2 + 1 , r 2 - 2 , - r 3 , - r 3 + 1 , r 3 - 2 respectively. It must satisfy the plane, hence r 1 = 3 2 , r 2 = - 3 2 , r 3 = + 1 . So points P , Q , R are 3 2 , - 1 2 , 1 , - 3 , - 1 2 , - 7 2 – 1,0 , – 1 respectively. P Q → = - 9 2 i ^ - 9 2 k ^ P R → = - 5 2 ı ^ + 1 2 j ^ - 2 k ^ Area = 1 2 P Q → × P R → = 1 8 i j ^ k ^ - 9 0 - 9 - 5 1 - 4 = 1 8 9 i ^ + 9 j ^ - 9 k ^ = 9 3 8 sq. units

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