Mathematics

Problem

Let

\mathbf{a}

\mathbf{b}

\mathbf{c}

are three vectors along the adjacent edges of a tetrahedron, if

|\mathbf{a}| = |\mathbf{b}| = |\mathbf{c}| = 2

and

\mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} = 2

, then volume of tetrahedron is a.

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

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

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

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