I guess the title really says it all. I'm reading "space-time algebra" by David Hestenes, and he explains the properties of the wedge product (area of parallelogram, antisymmetric, etc.) and it sounds just like the cross product to me. He then says clearly however that this is not to be confused eith the cross product since the definition of the a X b depends on the dimensionality of the vector space in which the vectors are embedded whereas a ^ b does not. I dont see how this is the case since he want a ^ b to have an orientation in the space in which it is embedded, if so, does it not also depend on the dimensionality of the surrounding space? P.S. If you have another way to show the distinction between them aside from his approach, I am open to, and interested in, hearing it. Thanks.