The CrossProduct(v1, v2) calling sequence computes the cross product (vector product) of v1 and v2, where v1 and v2 can be Vectors, vector fields, Student[VectorCalculus][Del], or Student[VectorCalculus][Nabla].

Note: You can enter vector fields as Vector-valued procedures or operators.

The Student[VectorCalculus] package has an &x cross product operator that you can use in place of the CrossProduct command. For example, CrossProduct(v1, v2) is equivalent to $\mathrm{v1}\&x\mathrm{v2}$.

Also, $\mathrm{Del}\&xF$ is equivalent to Curl(F).

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{VectorCalculus}\right]\right)\:$

$\mathrm{CrossProduct}\left(⟨a\,b\,c⟩\,⟨d\,e\,f⟩\right)$

$\left(bf-ce\right)e_x\+\left(-af+cd\right)e_y\+\left(ae-bd\right)e_z$

$⟨a\,b\,c⟩\&x⟨d\,e\,f⟩$

$\left(bf-ce\right)e_x\+\left(-af+cd\right)e_y\+\left(ae-bd\right)e_z$

$F≔\mathrm{VectorField}\left(⟨y\,-x\,0⟩\right)$

$F≔\left(y\right){\stackrel{\_}{e}}_x\+\left(-x\right){\stackrel{\_}{e}}_y\+\left(0\right){\stackrel{\_}{e}}_z$

$\mathrm{Del}\&xF$

$\left(0\right){\stackrel{\_}{e}}_x\+\left(0\right){\stackrel{\_}{e}}_y\+\left(\mathrm{-2}\right){\stackrel{\_}{e}}_z$

$\mathrm{CrossProduct}\left(\nabla \,F\right)$

$\left(0\right){\stackrel{\_}{e}}_x\+\left(0\right){\stackrel{\_}{e}}_y\+\left(\mathrm{-2}\right){\stackrel{\_}{e}}_z$

$\mathrm{SetCoordinates}\left(\mathrm{cylindrical}\right)$

${\mathrm{cylindrical}}_{r,\mathrm{\theta },z}$

$\mathrm{r1}≔\mathrm{RootedVector}\left(\left[2\,2\,1\right]\,\mathrm{root}=⟨1\,2\,3⟩\right)$

$\mathrm{r1}≔\left[\begin{array}{c}2\\ 2\\ 1\end{array}\right]$

$\mathrm{r2}≔\mathrm{RootedVector}\left(\left[3\,-1\,0\right]\,\mathrm{root}=⟨1\,2\,3⟩\right)$

$\mathrm{r2}≔\left[\begin{array}{c}3\\ \mathrm{-1}\\ 0\end{array}\right]$

$\mathrm{r1}\&x\mathrm{r2}$

$\left[\begin{array}{c}1\\ 3\\ \mathrm{-8}\end{array}\right]$