\begin{exercice}
Soit $ABCD$ un rectangle tel que $AB=4$ et $AD=1,5$. Soit $I$ le milieu de $[AB]$ et $J$ le point tel que $4\vv{DJ} = \vv{DC}$.
\begin{center}
 \begin{tikzpicture}[general, scale=1]
  %points
  \pointFigure{0}{0}{A}{color=black, below left};
  \pointFigure{4}{0}{B}{color=black, below right};
  \pointFigure{4}{1.5}{C}{color=black, above right};
  \pointFigure{0}{1.5}{D}{color=black, above left};
  \pointFigure{2}{0}{I}{color=black, below};
  \pointFigure{1}{1.5}{J}{color=black, above};
  %segments
  \draw (0,0)--(4,0)--(4,1.5)--(0,1.5)--(0,0);
  \draw (2,0)--(1,1.5);
 \end{tikzpicture}
\end{center}
Calculer les produits scalaires suivants :
\begin{colenumerate}{2}
 \item $\vv{AB} \cdot \vv{AC}$
 \item $\vv{AB} \cdot \vv{JI}$
 \item $\vv{BC} \cdot \vv{JI}$
 \item $\vv{AC} \cdot \vv{JI}$
\end{colenumerate}

\begin{corrige}
\begin{colenumerate}{2}
\item 16
\item 4
\item $-2.25$
\item $1,75$
\end{colenumerate}
\end{corrige}
\end{exercice}

