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.

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

$\mathrm{V1}≔⟨1\,2\,3⟩$

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

$\mathrm{V2}≔⟨2\,3\,4⟩$

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

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

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

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

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

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

The Student[LinearAlgebra][CrossProduct] and Student[LinearAlgebra][`&x`] commands were introduced in Maple 2020.

For more information on Maple 2020 changes, see Updates in Maple 2020.