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AP EAMCET201823 Apr 2018Morning ShiftMathematicsThree Dimensional GeometryActual

If the vertices of a A B C are A=(2,3,5) , B=(-1,3,2), C=(3,5,-2) , then the area of the A B C (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

The vertices of A B C are aligned & A=(2,3,5), B=(-1,3,2), C=(3,5,-2) & So, A B =(-1-2) i +(3-3) j +(2-5) k =-3 i -3 k & A C =(3-2) i +(5-3) j +(-2-5) k = i +2 j -7 k & Now, | A B A C |= | array ccc i & j & k -3 & 0 & -3 1 & 2 & -7 array | & = i (0+6)- j (21+3)+ k (-6+0) & =6 i -24 j -6 k & Now, | A B A C |= (6)^2+(-24)^2+(-6)^2 & = 36+576+36 & = 648 =18 2 & area of A B C= 1 2 | A B A C | & = 1 2 18 2 & =9 2 sq. units. & aligned

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