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MHT CET20242 May 2024Evening ShiftMathematicsVector AlgebraActual

If a = i +2 j +3 k and b = i ( a i )+ j ( a j )+ k ( a k ) then | b | is

Options

  1. A12
  2. B2 12
  3. C3 14
  4. D2 14

Correct answer

D. 2 14

Step-by-step solution

aligned & i ( a i ) & =( i i ) a -( i a ) i & =1( i +2 j +3 k )-[ i ( i +2 j +3 k )] i & = i +2 j +3 k - i =2 j +3 k aligned aligned & j ( a j )=( j j ) a -( j a ) j & = i +3 k & k ( a k )=( k k ) a -( k a ) k & = i +2 j & b =2 j +3 k + i +3 k + i +2 j & =2 i +4 j +6 k & | b |= 4+16+36 = 56 =2 14 aligned

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