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MHT CET202311 May 2023Evening ShiftMathematicsVector AlgebraActual

The unit vector perpendicular to each of the vectors a + b and a - b , where a = i + j + k and b =3 i -2 j +5 k is

Options

  1. A-14 i +4 j +10 k 312
  2. B14 i -4 j +10 k 312
  3. C14 i +4 j +10 k 312
  4. D-14 i -4 j +10 k 312

Correct answer

A. -14 i +4 j +10 k 312

Step-by-step solution

aligned a + b & =( i + j + k )+(3 i -2 j +5 k ) & =4 i - j +6 k a - b & =( i + j + k )-(3 i -2 j +5 k ) & =-2 i +3 j -4 k aligned Vector perpendicular to ( a + b ) and ( a - b ) is | array ccc i & j & k 4 & -1 & 6 -2 & 3 & -4 array |=-14 i +4 j +10 k Required unit vector is -14 i +4 j +10 k (-14)^2+4^2+(10)^2 = -14 i +4 j +10 k 312

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