Question The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit ....

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The edges of a parallelopiped are of unit length and
\( \mathrm{P} \)
are parallel to non-coplanar unit vectors \( \hat{a}, \hat{b}, \hat{c} \) such that \( \hat{a} \cdot \hat{b}=\hat{b} \cdot \hat{c} \cdot \hat{a}=\frac{1}{2} \). Then the volume of the parallelopiped is
(1) \( \frac{1}{\sqrt{2}} \)
(2) \( \frac{1}{2 \sqrt{2}} \)
(3) \( \frac{\sqrt{3}}{2} \)
(4) \( \frac{1}{\sqrt{3}} \)


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