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AP EAMCET202421 May 2024Morning ShiftMathematicsVector AlgebraActual

a = i - j + k , b = i + j -2 k , c =2 i -3 j - k , d =2 i + j + k are four vectors then ( a c ) ( b d )=

Options

  1. A2 i +19 j -11 k
  2. B-8 i +19 j -29 k
  3. C2 i + j -11 k
  4. D-8 i + j -29 k

Correct answer

D. -8 i + j -29 k

Step-by-step solution

aligned & a c = | array ccc i & j & k 1 & -1 & 1 2 & -3 & -1 array |=4 i +3 j - k & b d = | array ccc i & j & k 1 & 1 & -2 2 & 1 & 1 array |=3 i -5 j - k & ( a c ) ( b d )= | array ccc i & j & k 4 & 3 & -1 3 & -5 & -1 array |=-8 i + j -29 k aligned

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