The CrossProduct(U, V) function computes the cross product of Vectors U and V.

This command can also be entered using the infix notation $U\&xV$. No additional parameters can be provided in this case.

If W := CrossProduct(U, V), then W is a Vector with the following entries.

$\left[U_2{V}_3-U_3{V}_2\,-U_1{V}_3+U_3{V}_1\,U_1{V}_2-U_2{V}_1\right]$

If both U and V are row Vectors, their cross product is also a row Vector. Otherwise, a column Vector is returned.

The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Vector constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).

This function is part of the LinearAlgebra package, and so it can be used in the form CrossProduct(..) only after executing the command with(LinearAlgebra). However, it can always be accessed through the long form of the command by using LinearAlgebra[CrossProduct](..).

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$\mathrm{V1}≔⟨1\,2\,3⟩$

$\mathrm{V1}≔\left[\begin{array}{c}1\\ 2\\ 3\end{array}\right]$

$\mathrm{V2}≔⟨2\,3\,4⟩$

$\mathrm{V2}≔\left[\begin{array}{c}2\\ 3\\ 4\end{array}\right]$

$\mathrm{CrossProduct}\left(\mathrm{V1}\,\mathrm{V2}\right)$

$\left[\begin{array}{c}\mathrm{-1}\\ 2\\ \mathrm{-1}\end{array}\right]$

$\mathrm{V1}\&x\mathrm{V2}$

$\left[\begin{array}{c}\mathrm{-1}\\ 2\\ \mathrm{-1}\end{array}\right]$

$\mathrm{CrossProduct}\left(\mathrm{V1}\,\mathrm{V2}\,\mathrm{datatype}=\mathrm{float}\right)$

$\left[\begin{array}{c}\mathrm{-1.}\\ 2.\\ \mathrm{-1.}\end{array}\right]$