Magnitude of Scalar Triple Product equals Volume of Parallelepiped Contained by Vectors

Theorem
Let $\mathbf a, \mathbf b, \mathbf c$ be vectors in a vector space of $3$ dimensions:

Let $\mathbf a \cdot \left({\mathbf b \times \mathbf c}\right)$ denote the scalar triple product of $\mathbf a, \mathbf b, \mathbf c$.

Then $\left\lvert{\mathbf a \cdot \left({\mathbf b \times \mathbf c}\right)}\right\rvert$ equals the volume of the parallelepiped contained by $\mathbf a, \mathbf b, \mathbf c$.