[marctenbosch]

Ok I understand your question better, might update the article. Like the other commenter said, you can keep applying the geometric product more than once. To find what happens you can just work with the basis vectors.

So, you basically have three case: x (xx) = x (1) = x -> a vector

x (xy) = x (x.y + x^y) = x (x.y) + xxy = x (x.y) + y -> a vector

x (yz) = x (y.z + x^y) = x (y.z) + xyz -> a vector + a trivector. This only happens if the three vectors are independent, which can never be the case for -ava