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

Options

A. a) `(1)/(sqrt(2))` cu units
B. b) `(1)/(2sqrt(2))` cu units
C. c) `(sqrt(3))/(2)` cu units
D. d) `(1)/(sqrt(3))` cu units

Answer

A