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I wonder why angle between two vectors is alpha but not beta or 2*pi - alpha as below image:
Angle between two vectors http://img202.imageshack.us/img202/1936/80732467.png
Why the formular: cos(phi) = (vector a DOT vector b)/(|vector a| * |vector b|) always returns cos of alpha (but not beta or 2*pi - alpha?
So a (representative) of a vector is a directed segment and by definition the angle between two vectors is the one formed when going counter-clockwise from the first vector to the second. In your case this angle is
2*pi- alpha. Actaullycos(2*pi-alpha) = cos(-alpha) = cos(alpha)so if you care only about the cosine, whether you go clockwise or counter-clockwise won’t matter.