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JEE Main20238 Apr 2023Evening ShiftMathematicsVector AlgebraActual

The area of the quadrilateral A B C D with vertices A ( 2 , 1 , 1 ) , B ( 1 , 2 , 5 ) , C ( - 2 , - 3 , 5 ) and D ( 1 , - 6 , - 7 ) is equal to

Options

  1. A48
  2. B8 38
  3. C54
  4. D9 38

Correct answer

B. 8 38

Step-by-step solution

Given, The quadrilateral A B C D with vertices A ( 2 , 1 , 1 ) ,   B ( 1 , 2 , 5 ) ,   C ( - 2 , - 3 , 5 ) and D ( 1 , - 6 , - 7 ) Now finding, A B → = - i ^ + j ^ + 4 k ^ and A D → = - i ^ - 7 j ^ - 8 k ^ And plotting the diagram we get, Now we know that, Area of ∆ A B D is given by, = 1 2 i ^ j ^ k ^ - 1 1 4 - 1 - 7 8 = | 10 i ^ - 6 j ^ + 4 k ^ | = 2 38 Now finding, C B → = 3 i ^ + 5 j ^ and C D → = 3 i ^ - 3 j ^ - 12 k ^ So, Area of ∆ C B D = 1 2 i ^ j ^ k ^ 3 - 3 -

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