Re: vector products

[Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>]

Ludwik Kowalski wrote:

> I second Larry's and Robert's plea for a little tutorial "for
> the rest of us." ... Please assume that the reader is going
> to be a student in the first semester of the first non-calculus
> physics course. The student already knows kinematics, is
> familiar with [the addition of] 3D vectors and Newton's laws.
>
> Robert Cohen wrote:
>
> > It seems we can introduce the terminology of wedge
> > products at leasr when we deal with torque in physics
> > I, no?  I think that at that point the bivector idea actually
> > fits better than the psuedovector idea. I'd like someone
> > with more knowledge of GA to explain how one might
> > go about discussing torque in a freshmen physics class. ...

Let me observe that the hypothetical student would be confused by this:

> The fact is that the laws of electromagnetism are entirely
> reflection-symmetric. ... In particular, the Maxwell
> equations are commonly written using vector cross
> products, which depend on the right-hand rule.

It is clear that JohnD is talking to an ideal physics teacher,
not to a student in the first semester of the first non-calculus
physics course. He wrote:

> ... A bivector is basically a patch of area, with a direction
> of circulation marked on it. ... The bivector representing
> the magnetic field of a long, straight wire2 is shown in
> figure 3. ...

1) In other words a bivector is a scalar, not a vector. We
use a vector to represent a force but we use a bivector
to represent a torque. Is this correct?

2) Also E is a vector but B is not a vector. Right?

3) How would the magnetic flux be defined without
the idea that B is a vector ?

Ludwik Kowalski