\begin{definition}[Definition:Scalar Triple Product/Definition 2]
Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be vectors in a Cartesian $3$-space:
{{begin-eqn}}
{{eqn | l = \mathbf a
      | r = a_i \mathbf i + a_j \mathbf j + a_k \mathbf k
}}
{{eqn | l = \mathbf b
      | r = b_i \mathbf i + b_j \mathbf j + b_k \mathbf k
}}
{{eqn | l = \mathbf c
      | r = c_i \mathbf i + c_j \mathbf j + c_k \mathbf k
}}
{{end-eqn}}
where $\tuple {\mathbf i, \mathbf j, \mathbf k}$ is the standard ordered basis.
The '''scalar triple product''' of $\mathbf a$, $\mathbf b$ and $\mathbf c$ is defined and denoted as:
:$\sqbrk {\mathbf a, \mathbf b, \mathbf c} := \begin {vmatrix}
a_i & a_j & a_k \\
b_i & b_j & b_k \\
c_i & c_j & c_k \\
\end {vmatrix}$
where $\begin {vmatrix} \ldots \end {vmatrix}$ is interpreted as a determinant.
\end{definition}