The TripleScalarProduct command computes the triple scalar product of u, v, and w.

The triple scalar product can also be computed with BoxProduct, which is an alias of TripleScalarProduct.

The triple scalar product is given by DotProduct(u, CrossProduct(v, w)).

$\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right)\:$

$u≔⟨a\,b\,c⟩$

$u≔\left[\begin{array}{c}a\\ b\\ c\end{array}\right]$

$v≔⟨d\,e\,f⟩$

$v≔\left[\begin{array}{c}d\\ e\\ f\end{array}\right]$

$w≔⟨g\,h\,i⟩$

$w≔\left[\begin{array}{c}g\\ h\\ i\end{array}\right]$

$\mathrm{expand}\left(\mathrm{TripleScalarProduct}\left(u\,v\,w\right)\right)$

$aei-afh-bdi+bfg+cdh-ceg$

$\mathrm{expand}\left(\mathrm{BoxProduct}\left(w\,u\,v\right)\right)$

$aei-afh-bdi+bfg+cdh-ceg$

$\mathrm{expand}\left(v·\left(w\&xu\right)\right)$

$aei-afh-bdi+bfg+cdh-ceg$

The Student[MultivariateCalculus][TripleScalarProduct] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.