Joshua Zelinsky's blog on three things that you can't talk about in polite company: religion, politics and math.
Maybe it's just my research area, but I'm more comfortable thinking about the dot product of (unit) vectors than the angle between them. 0 is orthogonal, > 0 they point in the same direction, < 0 in the opposite direction. 0 makes more sense to me as the pivot than \pi/2.
Sure, if you're used to thinking about dot products of vectors that way. My point was just to note that this is an inner product (well, almost) in the first place and thus that you can think about it geometrically. If you don't need to take the inverse cosine to see it, then great. But regardless of which way you do it, I feel like the geometric viewpoint is underemphasized.
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