Hello Pat and all,
First, I tried to find the inner and outer products that seemed to make this work out well...
I'm much more interested in what you think about the 'justifications' of why I did what I did below...
As you can see, I believe I've taken the definitions that David Hestenes chose. I believe the defintion of inner product I've chosen is what the author of this webpage, http://www.iancgbell.clara.net/maths/geoalg1.htm#A18, calls the semi-commutative inner product, and the definition of outer product appears to be what the author of this webpage calls the "thin" outer product.
Going with these definitions of inner and outer products, I'm wondering if I can take the associated concept of parallelness with the inner product, and the associated concept of perpendicularly with the outer product, and generalize what I've done here to general multivectors.
Are my geometric and algebraic formulations correct? Is what I saying here essentially what Hestenes is saying... except perhaps more so in my own words...?
In what ways perhaps yes, and in what ways perhaps no...?