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AP EAMCET201726 Apr 2017Morning ShiftMathematicsVector AlgebraActual

If the volume of the tetrahedron formed by the coterminous edges a , b and c is 4 , then the volume of the parallelopiped formed by the coterminous edges a b , b c and c a is

Options

  1. A576
  2. B48
  3. C16
  4. D144

Correct answer

A. 576

Step-by-step solution

As we know, the volume of tetrahedron formed by the coterminous edges a , b and c , aligned & V= 1 6 [ array lll a & b & c array ] & 4= 1 6 [ array lll a & b & c array ] aligned Now, the volume of parallelopiped formed, by the coterminous edges a b , b c and c a . aligned V & = [ array lll a b & b c & c a array ] V & = [ array lll a & b & c array ]^2 ~V & =(24)^2=576 ( from Eq. (i)) aligned

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