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MHT CET202013 Oct 2020Evening ShiftMathematicsVector AlgebraActual

If a =2 i+3 j- k , b =-i+2 j-4 k and c =i+j+ k , then ( a b ) ( a c )=

Options

  1. A-74
  2. B64
  3. C-64
  4. D74

Correct answer

A. -74

Step-by-step solution

a b = | array ccc i & j & k 2 & 3 & -1 -1 & 2 & -4 array |= i (-12+2)- j (-8-1)+ k (4+3)=-10 i +9 j +7 k aligned a c &= | array ccc i & j & k 2 & 3 & -1 1 & 1 & 1 array |= i (3+1)- j (2+1)+ k (2-3)=4 i -3 j - k Here ( a b ) ( a c ) &=(-10 i +9 j +7 k ) (4 i -3 j - k ) &=(-10)(4)+9(-3)+7(-1) &=-40-27-7=-74 aligned

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