Math — Scalar & Vector Triple Products
Scalar triple product as a determinant and the BAC–CAB rule.
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\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c}) = \det\begin{pmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{pmatrix}
\mathbf{a}\times(\mathbf{b}\times\mathbf{c}) = \mathbf{b}(\mathbf{a}\cdot\mathbf{c}) - \mathbf{c}(\mathbf{a}\cdot\mathbf{b})
V = |\mathbf{a}\cdot(\mathbf{b}\times\mathbf{c})|
\mathbf{a}\times\mathbf{b} = -\mathbf{b}\times\mathbf{a}