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MHT CET20242 May 2024Evening ShiftMathematicsVector AlgebraActual

The unit vector which is orthogonal to the vector 5 i +2 j +6 k and is coplanar with the vectors 2 i + j + k and i - j + k is

Options

  1. A2 i -6 j + k 41
  2. B2 i -5 j 29
  3. C-3 j + k 10
  4. D2 i -8 j + k 69

Correct answer

C. -3 j + k 10

Step-by-step solution

Let a =5 i +2 j +6 k , b =2 i + j + k and c = i - j + k Then, required unit vectors are given by = a ( b c ) | a ( b c )| Now, a ( b c )=( a c ) b -( a b ) c aligned & =9(2 i + j + k )-18( i - j + k ) & =27 j -9 k aligned | a ( b c )|= 729+81 = 810 =9 10 Hence, required unit vectors are = 27 j -9 k 9 10 = 3 j - k 10

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