Angle between Two Vectors

Defining the angle. Let $\vec a=\vec{OA}$ and $\vec b=\vec{OB}$ be any two vectors, brought to a common initial point $O$. The angle between $\vec a$ and $\vec b$ is the angle $\theta$ between their directions at that common point — whether the two arrows visually converge or diverge from $O$, $\theta$ is measured the same way, and always satisfies $0\le\theta\le\pi.$

Parallel vectors. When $\theta=0$ (same direction) or $\theta=\pi$ (opposite directions), the vectors are parallel. …