To rotate a vector 
around an arbitrary vector 
the coordinate system has to be rotated such that the z-axis
is parallel to the vector 
,
then we rotate vector 
around the z-axis and
then rotate the coordinate system
to its original direction. The equations describing this transformation
are the following [5]:
vector 
:
the rotation matrix for rotating z-axis to be parallel to 
:
the rotation matrix for rotating 
by angle
around z-axis:
rotating vector 
by angle 
around 
:
when rotating vector 
around z-axis the
equation is simple:
