The edges of a parallelopiped are of unit length andare parallel to non-coplanar unit vectors $$\hat{a}, \hat{b}, \hat{c}$$ such that
$$\hat{a} . \hat{b} = \hat{b} . \hat{c} = \hat{c} . \hat{a} = \frac{1}{2}$$.
Then, the volume of the parallelopiped is

A

$$\frac{1}{\sqrt{2}}$$

B

$$\frac{1}{2\sqrt{2}}$$

C

$$\frac{\sqrt{3}}{2}$$

D

$$\frac{1}{\sqrt{3}}$$