If [ a b c ]=3 , then the volume (in cubic units) of the parallelopiped with 2 a + b , 2 b + c and 2 c + a as edges, is

Step-by-step solution

Given that, [abc] =3 Volume of the parallelopiped =[2 a + b 2 b + c +2 c + a ] aligned & =[2 a 2 ~b + c 2 c + a ]+[ b 2 b + c 2 c + a ] & =[2 a 2 ~b 2 c 2 a ]+[2 ac 2 c + a ] & +[b 2 b 2 c+a]+[b c 2 c+a] & =[2 a 2 b ~ 2 c ]+[2 a 2 b a ]+0+0+[ b c 2 c ]+[ b c a] & =8[a b c]+0+0+[a b c] & =9[ a b c ]=9 3=27 & aligned