I'm very aware of GA and multivectors and the usual equations that are included in GA texts, like the one-term form of Maxwell's equations. I'm specifically int

I'm very aware of GA and multivectors and the usual equations that are included in GA texts, like the one-term form of Maxwell's equations. I'm specifically interested in whether you know of a good reason to include the geometric product in all this. It seems to me that for the most part you can do all of the useful stuff without ever mentioning it, and the equations it produces tend to be very awkward (compute something, grade project, compute something else, project again...) -- it's very 'just so', and kinda feels like it's all using the wrong tool. But I haven't figured out what the better tool is yet.