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
![](../../Assets/Images/Img379.png)
and
![](../../Assets/Images/Img380.png)
are the vectors to be crossed and
![](../../Assets/Images/Img381.png)
,
![](../../Assets/Images/Img382.png)
, and
![](../../Assets/Images/Img383.png)
are the unit vectors along the
![](../../Assets/Images/Img384.png)
,
![](../../Assets/Images/Img385.png)
, and
![](../../Assets/Images/Img386.png)
axes:
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
![](../../Assets/Images/Img389.png)
: