If $\vec a, \vec b$ are vectors forming consecutive sides of a regular hexagon ABCDEF, then vector representing side CD is

$\vec b-\vec a$

Using vector addition in ΔABC, we have

$\vec{AB}+\vec{BC}=\vec{AC}⇒\vec a+\vec b=\vec {AC}$

Clearly, AD is parallel to BC and AD = 2BC

$∴\vec{AD}=2\vec b$

In ΔACD, we have

$\vec{AC}+\vec{CD}=\vec{AD}⇒\vec a+\vec b+\vec{CD}=2\vec b⇒\vec{CD}=\vec b-\vec a$