 
Summary: 12.4 Cross product
· The cross product is defined only for vectors in 3space, whereas the dot
product is defined for vectors in 2space and 3space.
Definition
1
u v×
u
If 1 2 3, ,u u ,u u= 1 2 3, ,v v then thev v=
cross product of u and v is
3 32 1 1
2 3 1 3 1 2
u uu u u u
u v i j k
v v v v v v
× =  + 2
or, equivalently,
2 3 3 2 3 1 1 3 1 2 2 1, ,u v u v u v u v u v u v u v×   =
v
Question 6/820: If
