Expressing vectors in an octagon

Hint:

$\vec{HG}=\vec{CD} = \vec{AD} - \vec{AC}$

$\vec{CD} || \vec{AF} \Rightarrow \vec{AF} = k\vec{CD}$

$\vec{AD} || \vec{BC} \Rightarrow \vec{AD} = k'\vec{BC}$

$\vec{AB} = \vec{AC} - \vec{BC} $

$\vec{AE} = \vec{AF} + \vec{AB} $

$\vec{AE} = \vec{AC} + \vec{AG} $