math - Angle between two vectors confused

Question

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?

Answer 1

因此，向量的（代表）是有向线段，根据定义，两个向量之间的角度是从第一个向量逆时针到第二个向量时形成的角度。在你的情况下，这个角度是2*pi- alpha。实际上cos(2*pi-alpha) = cos(-alpha) = cos(alpha)，如果您只关心余弦，那么顺时针还是逆时针方向都无关紧要。