\begin{exercice} On considère l'hexagone régulier $ABCDEF$ de centre $O$ et de côté 1 ci-dessous.

\begin{center}
\begin{tikzpicture}[general,scale=2]
\draw (1,0) -- (0.5,0.87) -- (-0.5,0.87) -- (-1,0) -- (-0.5,-0.87) -- (0.5,-0.87) -- (1,0);
\draw[dashed] (1,0) --  (-1,0) ;
\draw[dashed] (0.5,0.87) --  (-0.5,-0.87) ;
\draw[dashed] (-0.5,0.87) --  (0.5,-0.87) ;
\draw (1,0) node[right]{$A$} ;
\draw (0.5,0.87) node[above]{$B$} ;
\draw (-0.5,0.87) node[above]{$C$} ;
\draw (-1,0) node[left]{$D$} ;
\draw (-0.5,-0.87) node[below]{$E$} ;
\draw (0.5,-0.87) node[below]{$F$} ;
\draw (0,0.1) node[above]{$O$} ;
\end{tikzpicture}
\end{center}

En utilisant la méthode de votre choix, calculer les produits scalaires suivants :
\begin{colenumerate}{3}
  \item $\vv{OC}\cdot \vv{FO}$
  \item $\vv{OA}\cdot \vv{OB}$
  \item $\vv{OA}\cdot \vv{OF}$
  \item $\vv{CB}\cdot \vv{FA}$
  \item $\vv{OF}\cdot \vv{OD}$
  \item $\vv{CE}\cdot \vv{FB}$
  \item $\vv{EB}\cdot \vv{DF}$
  \item $\vv{CE}\cdot \vv{CA}$
  \item $\vv{BE}\cdot \vv{CO}$
\end{colenumerate}

\end{exercice}
