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AP EAMCET202022 Sep 2020Morning ShiftMathematicsVector AlgebraActual

If a , b , c are coterminous edges of a parallelopiped such that | array lll a a & a b & a c b a & b b & b c c a & c b & c c array |=16 , then find the volume of the parallelopiped

Options

  1. A32
  2. B16
  3. C4
  4. D8

Correct answer

C. 4

Step-by-step solution

It is given that, | array lll a a & a b & a c b a & b b & b c c a & c b & c c array |=16 Let a =a₁ I +a₂ J +a₃ k , b =b₁ I +b₂ J +b₃ k and c =c₁ i +c₂ j +c₃ k aligned & | array lll a a & a b & a c b a & b b & b c c a & c b & c c array | & = , array cc a₁^2+a₂^2+a₃^2 & a₁ b₁+a₂ b₂+a₃ b₃ b₁ a₁+b₂ a₂+b₃ a₃ & b₁^2+b₂^2+b₃^2 c₁ a₁+c₂ a₂+c₃ a₃ & c₁ b₁+c₂ b₂+c₃ b₃ array . & a₁ c₁+a₂ c₂+a₃ c₃ & b₁ c₁+b₂ c₂+b₃ c₃ & c₁^2+c₂^2+c₃^2 & aligned aligned & = | array lll a₁ & a₂ & a₃ b₁ & b₂ & b₃ c₁ & c₂ & c₃ array | | array lll a₁

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