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KCET2021MathematicsThree Dimensional Geometry

The area of the quadrilateral A B C D when A(0,4,1), B(2,3,-1), C(4,5,0) and D(2,6,2) is equal to

Options

  1. A9 sq units
  2. B18 sq units
  3. C27 sq units
  4. D81 sq units

Correct answer

A. 9 sq units

Step-by-step solution

In quadrilateral A B C D , given that A(0,4,1), B(2,3,-1), C(4,5,0) and D(2,6,2) . aligned & A B =2 i - j -2 k & A D =2 i +2 j + k & C B =-2 i -2 j - k & C D =-2 i + j +2 k aligned Required area of quadrilateral aligned &= 1 2 | A B A D |+ 1 2 | C B C D | &= 1 2 |3 i -6 j +6 k |+ 1 2 |-3 i +6 j -6 k | &= 1 2 3²+(-6)²+6² + 1 2 (-3)²+6²+(-6)² &= 1 2 9+ 1 2 9=9 sq units aligned

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