I'm given an exercise:
Given a regular hexagon whose vertices are $A, B, C, D, E, F$, and where $A_1, B_1, C_1, D_1, E_1, F_1$ are midpoints of $ \overline{AB}$, $ \overline{BC}$, $ \overline{CD}$, $ \overline{DE}$, $ \overline{EF}$, $ \overline{FA}$ respectively, prove that:
$\vec{AA_1} + \vec{BB_1} + \vec{CC_1} + \vec{DD_1} + \vec{AA_1} +\vec{EE_1} + \vec{FF_1} = \vec{0} $
Before I ask anything else, I want to point out that I'm not 100% sure that there should be a second $\vec{AA_1}$ in the equation, so it might be a typo. However, I tried doing the exercise in both cases and simply failed to do it. Could anyone help?