The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors a , b , c such that a b = b c = c a = 1 2 . Then, the volume of the parallelopiped is

Step-by-step solution

The volume of the parallelopiped with coterminus edges as a , b , c is given by [ a b c ]= a ( b c ) aligned & Now, [ a b c ]^2= | array ccc a a & a b & a c b a & b b & b c c a & c b & c c array |= | array ccc 1 & 1 / 2 & 1 / 2 1 / 2 & 1 & 1 / 2 1 / 2 & 1 / 2 & 1 array |= 1 2 & [ a b c ]^2= 1 2 & aligned Thus, the required volume of the parallelopiped = 1 2 cu units