1. The problem statement, all variables and given/known data It's not a homework question but a doubt I have. Say I want to write [itex]\vec A \times \vec B[/itex] in the basis of the cylindrical coordinates. I already know that the cross product is a determinant involving [itex]\hat i[/itex], [itex]\hat j[/itex] and [itex]\hat k[/itex]. And that it's worth in my case [itex](A_yB_z-B_yA_z) \hat i +(A_xB_z-B_xA_z)\hat j+(A_xB_y-B_xA_y)\hat k[/itex]. In order to reach what I'm looking for, can I "translate" [itex]A_x[/itex], [itex]B_y[/itex], etc. into cylindrical coordinates and then replace [itex]\hat i[/itex], [itex]\hat j[/itex] and [itex]\hat z[/itex] by what they are worth when translated in cylindrical coordinates and in function of the cylindrical unit vectors [itex]\hat r[/itex], [itex]\hat \theta[/itex] and [itex]\hat z[/itex]?