In mathematics there are a number of ways to multiply two vectors. The most common is the dot product, which works for any two vectors of the same size. In three dimensions there's the cross product, while in two dimensions there's the perp dot product, sort of equivalent to the cross product.
But they all have the weakness that they are not invertible. Given the cross product
and knowing c and another vector it isn't possible to calculate the third vector (c × c = 0, so given a solution all points on a line through this solution parallel to c are also solutions).
