\begin{exercice}
On considère un cube $ABCDEFGH$ de côté 1. Soient $I$ le milieu de $[EH]$ et $J$ le centre de la face $CDHG$.
\vspace{-1em}
\begin{center}
 	\def \dx {-0.4}
	\begin{tikzpicture}[general, scale=1.5]
	%points
	\coordinate (A) at (0,0); \draw (A) node[above left] {$A$};
	\coordinate (B) at (\dx,-0.5); \draw (B) node[below left] {$B$};
	\coordinate (C) at (1+\dx,-0.5); \draw (C) node[below] {$C$};
	\coordinate (D) at (1,0); \draw (D) node[right] {$D$};
	\coordinate (E) at (0,1); \draw (E) node[above left] {$E$};
	\coordinate (F) at (\dx,0.5); \draw (F) node[left] {$F$};
	\coordinate (G) at (1+\dx,0.5); \draw (G) node[right] {$G$};
	\coordinate (H) at (1,1); \draw (H) node[above right] {$H$};
	\coordinate (I) at (0.5,1); \draw (I) node[above right] {$I$}; \draw (I) node {$\times$};
	\coordinate (J) at ({(2+\dx)/2},0.25); \draw (J) node[right] {$J$};
	%arêtes
	\draw (F)--(B)--(C)--(D)--(H)--(G)--(C); \draw (G)--(F)--(E)--(H);
	\draw[dashed] (A)--(B); \draw[dashed] (A)--(D); \draw[dashed] (A)--(E);
	%diagonales de CDGH
	\draw[thin] (C)--(H); \draw[thin] (G)--(D);
	\end{tikzpicture}
\end{center}

\vspace{-2em}

\begin{enumerate}
 \item Donner les coordonnées du point $G$ dans le repère :
 \begin{colenumerate}{2}
  \item $(A\, ; \vv{AB}, \vv{AD}, \vv{AE})$
  \item $(C\, ; \vv{CB}, \vv{CD}, \vv{CG})$
  \item $(H\, ; \vv{HE}, \vv{HD}, \vv{HG})$
  \item $(F\, ; \vv{FB}, \vv{FG}, \vv{FE})$
 \end{colenumerate}
 \item Même question avec le point $B$.
 \item Même question avec le point $J$.
\end{enumerate}
\begin{corrige}
\begin{enumerate}
 \item \begin{colenumerate}{2}
  \item $(1\,; 1\,; 1)$
  \item $(0\,; 0\,; 1)$
  \item $(0\,; 0\,; 1)$
  \item $(0\,; 1\,; 0)$
 \end{colenumerate}
 
 \item \begin{colenumerate}{2}
  \item $(1\,; 0\,; 0)$
  \item $(1\,; 0\,; 0)$
  \item $(1\,; 1\,; 1)$
  \item $(1\,; 0\,; 0)$
 \end{colenumerate}
 
 \item \begin{colenumerate}{2}
  \item $\left(\frac{1}{2}\,; 1\,; \frac{1}{2}\right)$
  \item $\left(0\,; \frac{1}{2}\,; \frac{1}{2}\right)$
  \item $\left(0\,; \frac{1}{2}\,; \frac{1}{2}\right)$
  \item $\left(\frac{1}{2}\,; 1\,; \frac{1}{2}\right)$
 \end{colenumerate}
\end{enumerate}
\end{corrige}
\end{exercice}

