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Manipal MET2010MathematicsVector Algebra

If V is the volume of the parallelopiped having three coterminus edges as a , b and c , then the volume of the parallelopiped having three coterminus edge as aligned & =( a a ) a +( a b ) b +( a c ) c & =( a b ) a +( b b ) b +( b c ) c & =( a c ) a +( b c ) b +( c c ) c is aligned

Options

  1. AV^3
  2. B3 V
  3. CV^2
  4. D2 V

Correct answer

A. V^3

Step-by-step solution

We have, |[ a b c ]|=V Let V₁ be the volume of parallelopiped formed by the vectors , and . Then, V₁=|[ ]| V₁= | array lll a a & a b & a c a b & b b & b c a c & b c & c c array |[ a b c ] V₁=[ a b c ]^2[ a b c ] V₁=[ a b c ]^3 V₁=V^3

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