Editing Cross product (section)

=== The paradox of the orthonormal basis ===
Let ('''i''', '''j''', '''k''') be an orthonormal basis. The vectors '''i''', '''j''' and '''k'''  do not depend on the orientation of the space. They can even be defined in the absence of any orientation. They can not therefore be axial vectors. But if '''i''' and '''j''' are polar vectors, then '''k''' is an axial vector for '''i''' × '''j''' = '''k''' or '''j''' × '''i''' = '''k'''. This is a paradox.

"Axial" and "polar" are ''physical'' qualifiers for ''physical'' vectors; that is, vectors which represent ''physical'' quantities such as the velocity or the magnetic field. The vectors '''i''', '''j''' and '''k''' are mathematical vectors, neither axial nor polar. In mathematics, the cross-product of two vectors is a vector. There is no contradiction.