Answer
Explanation given below.
Work Step by Step
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)
