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AP EAMCET201825 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

If the vertices of Δ ABC are A = ( 2 , 3 , 5 ) , B = ( - 1 , 3 , 2 ) , C = ( 3 , 5 , - 2 ) , then the area of the Δ ABC (in sq. units) is

Options

  1. A6 2
  2. B8 3
  3. C9 2
  4. D8 2

Correct answer

C. 9 2

Step-by-step solution

Given: A ≡ ( 2 , 3 , 5 ) ,   B ≡ ( - 1 , 3 , 2 ) ,   C ≡ ( 3 , 5 , - 2 ) Now, O A → = 2 i ^ + 3 j ^ + 5 k ^ O B → = - i ^ + 3 j ^ + 2 k ^ O C → = 3 i ^ + 5 j ^ - 2 k ^ Now, A B → = O B → - O A → = - 3 i ^ - 3 k ^ Similarly, A C → = i ^ + 2 j ^ - 7 k ^ Now, A B → × A C → = i ^ j ^ k ^ - 3 0 - 3 1 2 - 7 = 6 i ^ - 24 j ^ - 6 k ^ Area of triangle is = 1 2 A B → × A C → = 1 2 36 + 36 + 576 = 648 2 = 9 2 sq. units

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