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## Main Question or Discussion Point

When using cartesian coordinates, I use the following expressions to calculate the cross product of the basis vectors:

[tex]i \times j = k[/tex]

[tex]j \times k = i[/tex]

[tex]k \times i = j[/tex]

[tex]j \times i = -k[/tex]

[tex]k \times j = -i[/tex]

[tex]i \times k = -j[/tex]

Can I do the same in polar coordinates? How could I write the cross product for the vectors [tex]r[/tex], [tex]\theta[/tex] and [tex]z[/tex]?

[tex]i \times j = k[/tex]

[tex]j \times k = i[/tex]

[tex]k \times i = j[/tex]

[tex]j \times i = -k[/tex]

[tex]k \times j = -i[/tex]

[tex]i \times k = -j[/tex]

Can I do the same in polar coordinates? How could I write the cross product for the vectors [tex]r[/tex], [tex]\theta[/tex] and [tex]z[/tex]?

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