Why is the angle between vectors restricted?

Question

Why is the calculated angle between two vectors always between $\pi$ and $0$.

Is this due to the limitations of $\arccos\theta$ or is it because angles between vectors is described to be the smaller one?

Answer 1

It's a matter of tradition and simplicity.

Each pair of vectors defines two angles. One of them is between $0$ and $\pi$ and the other is between $\pi$ and $2\pi$. Since their sum is $2\pi$, we only really need to tell one of the two angles, and we decide, for simplicity, to always report the smaller of the two.

Answer 2

There are angles of all possible degrees. In context with angles in a triangle however, we have $0\le \theta \le \pi$.