Definition talk:Angle Between Vectors

Is $0 \le \theta \le \pi$ a theorem or a definition, do you guys think? --GFauxPas 14:00, 19 March 2012 (EDT)

I think it's just a common convention, if I'm not mistaken. Abcxyz 14:05, 19 March 2012 (EDT)

Yes, it's a useful convention, but any $[2k\pi.. (2k+1)\pi]$ would work of course. --Lord_Farin 14:23, 19 March 2012 (EDT)

Shouldn't this be a proof not a definition? --prime mover 15:58, 20 March 2012 (EDT)

Well if it's a proof then I need another definition of "angle between two vectors". I've seen the definition as $\theta := \arccos \dfrac {\mathbf u \cdot \mathbf v}{||\mathbf u|| \ ||\mathbf v||}$, but that seems much more natural as a theorem rather than as a definition. --GFauxPas 16:37, 20 March 2012 (EDT)

The advantage of the algebraic definition is that it does not rely on drawing a certain picture in $\R^2$ which is bound to interfere with intuition. But my preoccupation may also have risen from the fact that I hadn't seen the geometrical definition before. --Lord_Farin 16:41, 20 March 2012 (EDT)