solution

Since each parallelopied consists of four tetrahedron of equal volume, the volume of the the tetrahedron formed by the vectors ${\bf u, v}$ and ${\bf w}$ is $\frac { 1} { 4} \vert \det \left( \left[ \begin{array}{rrr} u_1 & u_2 & u_3 \\ v_1 & v_2 & v_3 \\ w_1 & w_2 & w_3 \\ \end {array} \right]\right) \vert$.