Parallelepiped

In Euclidean geometry, a parallelepiped is a three-dimensional figure (a polyhedron) having six sides (a hexahedron or prism). All six sides are parallelograms. Opposing sides are parallel and therefore all opposing sides are also congruent.

Given a parallelepiped whose edges are formed by the vectors $\mathbf{v},\mathbf{u},\mathbf{w}$ , the volume of the parallelepiped is the scalar triple product of the three vectors:

$\mathbf{v}\times\mathbf{w}\cdot\mathbf{u}= \begin{vmatrix} \mathbf{v}_x&\mathbf{w}_x&\mathbf{u}_x\\ \mathbf{v}_y&\mathbf{w}_y &\mathbf{u}_y\\ \mathbf{v}_z&\mathbf{w}_z &\mathbf{u}_z\\ \end{vmatrix}$