## Thomas' Calculus 13th Edition

Two vectors are equal if they have the same direction and have the same magnitude (length). So, two directed line segments $\overrightarrow{AB}$ and $\overrightarrow{CD}$ represent the same vector if 1. The directions (unit vectors), $\displaystyle \frac{\overrightarrow{AB}}{|\overrightarrow{AB}|}$ and $\displaystyle \frac{\overrightarrow{CD}}{|\overrightarrow{CD}|}$ are equal and 2. $|\overrightarrow{AB}|$=$|\overrightarrow{CD}|\qquad$; that is, they have equal magnitudes (lengths)