Let a be the direction vector 
Let b be the direction vector 

Cross Product (final answer is a vector):
a × b =  ×  =
< a2*b3 - a3*b2,
  a3*b1 - a1*b3,
  a1*b2 - a2*b1 >
-or-
a × b = (|a||b|sinθ) n, where θ is the angle between the two vectors
                        and n is the unit vector normal (perpendicular) to 
                        the plane created by a and b.