The wedge product (or "outer product" in geometric algebra) generalizes the cross product and works in any number of dimensions, in the sense that the cross pro

The wedge product (or "outer product" in geometric algebra) generalizes the cross product and works in any number of dimensions, in the sense that the cross product in 3D is just the Hodge star of the wedge product. The cross product gives a vector perpendicular to the plane generated by two vectors, whereas the wedge product gives an object representing that plane directly, and the Hodge star then mapping it to its orthogonal complement.