Can you have axial vectors in a 2D space?

[touqra]

Can you have axial vectors in a 2D space?

 

[HallsofIvy]

In a sense. The "axial vector" would be perpendicular to the plane.

 

[robphy]

I think such an object would be called a "twisted vector" or "odd vector".
See
http://www.ucolick.org/~burke/forms/draw.ps
http://www.ucolick.org/~burke/forms/twisted.html
from Bill Burke's pages http://www.ucolick.org/~burke/home.html
(You may need a postscript viewer like http://www.cs.wisc.edu/~ghost/gsview/ )
See also http://www.icm.edu.pl/edukacja/mat/axial.php