Definition:Scalar Triple Product/Definition 2

Definition
Let $\mathbf a$, $\mathbf b$ and $\mathbf c$ be vectors in a Cartesian $3$-space:

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.

Also see

 * Equivalence of Definitions of Scalar Triple Product