If [ a b c ]=4 , then the volume (in cubic units) of the parallelepiped with a +2 b , b +2 c and c +2 a as coterminal edges, is

Step-by-step solution

We have a ( b c )=4 Volume of required parallelepiped is aligned & ( a +2 b ) [( b +2 c ) c +2 a ] & =( a +2 b ) [( b c )+2( c c )+2( b a )+4( c a )] & = a ( b c )+ a (0)+2 a ( b a )+4 a ( c a )+2 b ( b c ) & +4 b (0)+4 b ( b a )+8 b ( c a ) & = a ( b c )+0+0+0+0+0+0+8 a ( b c ) & =9[ a ( b c )]=9(4)=36 aligned