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Student[MultivariateCalculus]

 TripleScalarProduct
 return the triple scalar product of three vectors

 Calling Sequence TripleScalarProduct(u, v, w) BoxProduct(u, v, w)

Parameters

 u, v, w - three-dimensional Vectors with algebraic entries

Description

 • 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)).

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right):$
 > $u≔⟨a,b,c⟩$
 ${u}{≔}\left[\begin{array}{c}{a}\\ {b}\\ {c}\end{array}\right]$ (1)
 > $v≔⟨d,e,f⟩$
 ${v}{≔}\left[\begin{array}{c}{d}\\ {e}\\ {f}\end{array}\right]$ (2)
 > $w≔⟨g,h,i⟩$
 ${w}{≔}\left[\begin{array}{c}{g}\\ {h}\\ {i}\end{array}\right]$ (3)
 > $\mathrm{expand}\left(\mathrm{TripleScalarProduct}\left(u,v,w\right)\right)$
 ${a}{}{e}{}{i}{-}{a}{}{f}{}{h}{-}{b}{}{d}{}{i}{+}{b}{}{f}{}{g}{+}{c}{}{d}{}{h}{-}{c}{}{e}{}{g}$ (4)

The triple scalar product is invariant under circular shift of the arguments.

 > $\mathrm{expand}\left(\mathrm{BoxProduct}\left(w,u,v\right)\right)$
 ${a}{}{e}{}{i}{-}{a}{}{f}{}{h}{-}{b}{}{d}{}{i}{+}{b}{}{f}{}{g}{+}{c}{}{d}{}{h}{-}{c}{}{e}{}{g}$ (5)
 > $\mathrm{expand}\left(v\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}w&xu\right)$
 ${a}{}{e}{}{i}{-}{a}{}{f}{}{h}{-}{b}{}{d}{}{i}{+}{b}{}{f}{}{g}{+}{c}{}{d}{}{h}{-}{c}{}{e}{}{g}$ (6)

Compatibility

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