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COMEDK2020MathematicsThree Dimensional Geometry

A vector perpendicular to the plane containing the points A(1,-1,2), B(2,0,-1), C(0,2,1) is

Options

  1. A8 i +4 j +4 k
  2. B4 i +8 j -4 k
  3. Ci + j - k
  4. D3 i + j +2 k

Correct answer

A. 8 i +4 j +4 k

Step-by-step solution

We have, A(1,-1,2), B(2,0,-1) and C(0,2,1) A B = 2-1) i +(0-(-1)) j +(-1-2) k= i + j -3 k and A C=(0-1) i +(2-(-1)) j +(1-2) k=- i +3 j - k Now, required vector = A B A C aligned &= | array ccc i & j & k 1 & 1 & -3 -1 & 3 & -1 array | &=8 i +4 j +4 k aligned

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