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Student[LinearAlgebra]

 CrossProduct
 compute the cross product of two Vectors
 &x
 compute the cross product of two Vectors

 Calling Sequence CrossProduct(U, V, options) U &x V

Parameters

 U, V - three-dimensional Vectors options - (optional) parameters; for a complete list, see LinearAlgebra[CrossProduct]

Description

 • The CrossProduct(U, V) function computes the cross product of Vectors U and V.
 This command can also be entered using the infix notation $U\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&x\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}V$. 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.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{LinearAlgebra}\right):$
 > $\mathrm{V1}≔⟨1,2,3⟩$
 ${\mathrm{V1}}{≔}\left[\begin{array}{c}{1}\\ {2}\\ {3}\end{array}\right]$ (1)
 > $\mathrm{V2}≔⟨2,3,4⟩$
 ${\mathrm{V2}}{≔}\left[\begin{array}{c}{2}\\ {3}\\ {4}\end{array}\right]$ (2)
 > $\mathrm{CrossProduct}\left(\mathrm{V1},\mathrm{V2}\right)$
 $\left[\begin{array}{c}{-1}\\ {2}\\ {-1}\end{array}\right]$ (3)
 > $\mathrm{V1}\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&x\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\mathrm{V2}$
 $\left[\begin{array}{c}{-1}\\ {2}\\ {-1}\end{array}\right]$ (4)
 > $\mathrm{CrossProductPlot}\left(\mathrm{V1},\mathrm{V2}\right)$

Compatibility

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