If the volume of a tetrahedron whose conterminous edges are a + b , b + c , c + a is 24 cubic units, then the volume of parallelepiped whose coterminous edges are a , b , c is

Step-by-step solution

As per data given, we write aligned & 24= 1 6 ( a + b ) [( b + c ) ( c + a )] & = 1 6 ( a + b ) [( b c )+( b + a )+( c a )] [ c c =0] & 144=[ a ( b c )]+[ b ( b c )]+[ b ( b a )]+[ a ( c a )]+[ b ( c a )] & =[ a ( b c )]+0+0+0+0[ b ( c a )] & =2[ a ( b c )] [ b ( c a )= a ( b c )] & a ( b c )=72, i.e. volume of parallelepiped with & conterminous edges a , b , c . aligned