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Manipal MET2016MathematicsThree 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. A4 i +8 j -4 k
  2. B3 i + j +2 k
  3. C8 i +4 j +4 k
  4. Di + j - k

Correct answer

C. 8 i +4 j +4 k

Step-by-step solution

We know that a vector perpendicular to the plane containing the point A , B and C is given by A B + B C + C A . Given, A = i - j +2 k , =2 i +0 j - k and C =0 i +2 j + k Now, A B = | array ccc i & j & k 1 & -1 & 2 2 & 0 & -1 array |= i +5 j +2 k B C = | array ccc i & j & k 2 & 0 & -1 0 & 2 & 1 array |=2 i -2 j +4 k C A = | array ccc i & j & k 0 & 2 & 1 1 & -1 & 2 array |=5 i + j -2 k Thus, A B + B C + C A aligned & =( i +5 j +2 k )+(2 i -2 j +4 k )+(5 i + j -2 k ) & =8 i +4 j +4 k aligned

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