Developer: RhinoScript
Summary: Demonstrates how to calculate the angle between two vectors.

I know that I can calculate the angle between two lines using RhinoScript's Angle2 method. But, when I am dealing with 3-D vectors, I always have to calculate the points that define the two lines. Is there a way to determine the angle between two 3-D vectors without having to do this?

Yes there is. See the following example function.

 ' Description: 
 '  Calculates the angle between two 3-D vectors.
 ' Parameters:
 '   v0 - [in] - the first vector.
 '   v1 - [in] - the second vector.
 ' Returns: 
 '   the angle in degrees.

 Function VectorAngle(v0, v1)
 
   Dim u0  : u0  = Rhino.VectorUnitize(v0)
   Dim u1  : u1  = Rhino.VectorUnitize(v1)  
   Dim dot : dot = Rhino.VectorDotProduct(u0, u1)
 
   ' Force the dot product of the two input vectors to 
   ' fall within the domain for inverse cosine, which 
   ' is -1 <= x <= 1. This will prevent runtime 
   ' "domain error" math exceptions.
   If (dot < -1.0) Then
     dot = -1.0
   ElseIf (dot > 1.0) Then
     dot = 1.0
   End If
 
   VectorAngle = Rhino.ToDegrees(Rhino.ACos(dot))
 
 End Function