Why is it okay to translate them both to be starting from the origin [b]and[/b] why is it arbitrary that I have translated them to the origin?
To consider the angle between two lines, we only need the direction vectors, which do not have a fixed position, therefore can be translated anywhere. In order to find the angle between them, I need translate these vectors to be coplanar (in the same plane), any two vectors that share a common point will be coplanar, as a plane is defined by two non-parallel vectors.