Different Types of Vectors

Vectors are sorted into several useful families based on how their magnitudes and directions compare:

• Equal vectors: $\vec A$ and $\vec B$ are equal when they have the same magnitude, the same direction, and represent the same physical quantity. Two arrows drawn at completely different places on a page are still 'the same vector' if they have identical length and point the same way — position on the page does not matter for a free vector.
• Collinear vectors: vectors that act along the same straight line (or along parallel lines), so the angle between them is either $0°$ or $180°$. There are two collinear sub-cases:
• Parallel vectors: $\vec A$ and $\vec B$ point in the same direction along the same or parallel lines — the angle between them is $0°$.
• Anti-parallel vectors: $\vec A$ and $\vec B$ point in opposite directions along the same or parallel lines — the angle between them is $180°$.
• Unit vector: a vector divided by its own magnitude, i.e. a vector of magnitude exactly $1$, used purely to record a direction. The unit vector along $\vec A$ is written $\hat A$ (read 'A cap' or 'A hat'), and by definition

so a unit vector always specifies only the direction of a vector quantity, never its size. …