The cross product is a vector-vector operation that, unlike the dot product, yields another vector. The easiest way to compute the cross product is using a 3x3 determinant (one of the many applications of the determinant) where 
and 
are the vectors to be crossed and 
, 
, and 
are the unit vectors along the 
, 
, and 
axes: 
and are the vectors to be crossed and , , and are the unit vectors along the , , and axes: Object could not be loaded.
Figure 3-1. Geometry of the Cross Product
It should be clear from the definition that the cross product is not commutative and that, in fact, reversing the order simply negates the result: 
Excercise 3-9.
Determine the cross product 
: 
: 