Ok... I'll leave the comment to stand but apparently I just needed to scroll a tiny bit more and get an answer here[0]. The seven-dimensional cross product i

Ok... I'll leave the comment to stand but apparently I just needed to scroll a tiny bit more and get an answer here[0]. The seven-dimensional cross product is one way of generalizing the cross product to other than three dimensions, and it is the only other bilinear product of two vectors that is vector-valued, orthogonal, and has the same magnitude as in the 3D case.[2] In other dimensions there are vector-valued products of three or more vectors that satisfy these conditions, and binary products with bivector results. [0] https://en.m.wikipedia.org/wiki/Seven-dimensional_cross_product https://en.m.wikipedia.org/wiki/Seven-dimensional_cross_prod...