“Given the properties of bilinearity, orthogonality and magnitude, a nonzero cross product exists only in three and seven dimensions.”
why only 3 and 7? what's the relationship with quaternions and octonions?
in a similar vein,
https://en.m.wikipedia.org/wiki/Exceptional_object
“Given the properties of bilinearity, orthogonality and magnitude, a nonzero cross product exists only in three and seven dimensions.”