The right-hand rule determines the orientation of the cross product 
for nonparallel vectors 
and 
. Place the vectors
tail-to-tail, extend the fingers of the right hand in the direction of 
, and curl them toward 
through the smaller angle between
the vectors. The extended thumb then points in the direction
of 
.
A three-dimensional coordinate system in which the axes satisfy the right-hand rule is called a right-handed coordinate system, while one that does not is called a left-handed coordinate system.
