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AP EAMCET202317 May 2023Morning ShiftMathematicsVector AlgebraActual

If OA =2 i - j + k , O B =3 i - k and O C =2 j +3 k are the position vectors of the points A, B and C , then a unit vector perpendicular to the plane containing A , B and C is

Options

  1. A8 i -4 j +2 k 2 21
  2. B6 i +2 j +3 k 7
  3. C9 i +2 j +6 k 11
  4. D8 i +2 j +5 k 93

Correct answer

D. 8 i +2 j +5 k 93

Step-by-step solution

aligned & A B = O B - O A = i + j -2 k & A C =-2 i +3 j +2 k aligned A B and A C lies on the plane. Then A B A C will be perpendicular to the plane. Now, n = A B A C = | array ccc i & j & k 1 & 1 & -2 -2 & 3 & 2 array |=8 i +2 j +5 k The unit vector perpendicular to the plane is n = n | n | = 8 i +2 j +5 k 64+4+25 = 8 i +2 j +5 k 93

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