
\begin{enumerate}
\item 
\begin{itemize}
\item $\begin{aligned}[t]
3\vv{CE} = 2\vv{BE}+3\vv{AB} & \iff 3\vv{CE} = 2\big(\vv{BC}+\vv{CE}\big)+3\vv{AB}\\& \iff 3\vv{CE} = 2\vv{BC}+2\vv{CE}+3\vv{AB}\\
& \iff \boxed{\vv{CE} = 2\vv{BC} + 3\vv{AB}}
\end{aligned}$

\item $\begin{aligned}[t]
3\vv{FC}=2\vv{FB} & \iff 3\vv{FC} = 2\big(\vv{FC}+\vv{CB}\big)\\
& \iff 3\vv{FC} = 2\vv{FC}+2\vv{CB}\\
& \iff \vv{FC} = 2\vv{CB}\\
& \iff \boxed{\vv{CF} = 2\vv{BC}}
\end{aligned}$
\end{itemize}

\item $\begin{aligned}[t]
\vv{AE} & = \vv{AD} + \vv{DF} + \vv{FC} + \vv{CE}\\
        & = 3\vv{BA} + \vv{DF} - 2\vv{BC} + 3\vv{AB} + 2\vv{BC}\\
        & = \underbrace{ 3\vv{BA} + 3\vv{AB} }_{=\vv{0}}  \underbrace{- 2\vv{BC}  + 2\vv{BC}}_{=\vv{0}} + \vv{DF}\\
        & = \vv{DF}.
\end{aligned}$

\medskip

Ainsi, $ADFE$ est un parallélogramme.
\end{enumerate}
