> Also, why the need o a dual(e12, e02, e01) to represent a point when in vector it's just a (e0, e1, e2). This is just counterinuitive.

It seems like it isn't needed, but it hasn't all been wrapped up into an easy to understand package yet:

http://terathon.com/blog/projective-geometric-algebra-done-r...

http://terathon.com/blog/symmetries-in-projective-geometric-...