For example, when we teach dot product of vectors A.B, we teach them that it is B.A — again the order has no meaning. On the other hand, with a cross product, we cannot do that AxB is not the same as BxA. That distinction is absolutely essential in understanding the concept here. In sclar multiplication and dot products, equal and equivalence are the same. Medicine dosage is a time dependent function, we can only equate here for the total dose rather than incremental dose.