\begin{definition}[Definition:Scalar Triple Product/Definition 1]
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:
:$\sqbrk {\mathbf a, \mathbf b, \mathbf c} := \mathbf a \cdot \paren {\mathbf b \times \mathbf c}$
where:
:$\cdot$ denotes dot product
:$\times$ denotes vector cross product.
\end{definition}