\begin{minipage}{6cm}
\begin{tikzpicture}
\definecolor{ttzzqq}{rgb}{0.2,0.6,0}
\definecolor{qqwwzz}{rgb}{0,0.4,0.6}
\definecolor{ffqqqq}{rgb}{1,0,0}
\definecolor{ududff}{rgb}{0.30196078431372547,0.30196078431372547,1}
\definecolor{xdxdff}{rgb}{0.49019607843137253,0.49019607843137253,1}
\node[fill = white] (img) {
\begin{tikzpicture}
\draw  (1,4)-- (4,4);
\draw  (4,4)-- (3,3);
\draw  (3,3)-- (0,3);
\draw  (0,3)-- (1,4);
\draw  (0,3)-- (0,0);
\draw  (0,0)-- (3,0);
\draw  (3,0)-- (3,3);
\draw  (4,4)-- (4,1);
\draw  (4,1)-- (3,0);
\draw [dash pattern=on 1pt off 1pt] (1,4)-- (1,1);
\draw [dash pattern=on 1pt off 1pt] (1,1)-- (0,0);
\draw [dash pattern=on 1pt off 1pt] (1,1)-- (4,1);
\draw [dash pattern=on 1pt off 1pt,color=qqwwzz] (0,0)-- (4,2.5);
\draw [color=xdxdff] (0,0)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=xdxdff] (-0.34,-0.19) node {$A$};
\draw [color=ududff] (1,1)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=ududff] (0.72,1.23) node {$B$};
\draw [color=ududff] (4,1)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=ududff] (4.28,1.09) node {$C$};
\draw [color=xdxdff] (3,0)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=xdxdff] (3.16,-0.27) node {$D$};
\draw [color=xdxdff] (0,3)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=xdxdff] (-0.26,3.49) node {$E$};
\draw [color=ududff] (1,4)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw [color=purple] (2,3)-- ++(-1.5pt,-1.5pt) -- ++(3pt,3pt) ++(-3pt,0) -- ++(3pt,-3pt) node[below] {$K$};
\draw[color=ttzzqq] (2.48,1.93) node {$J$};
\draw[color=ududff] (1.02,4.35) node {$F$};
\draw [color=ududff] (4,4)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=ududff] (4.16,4.27) node {$G$};
\draw [color=ududff] (3,3)-- ++(-0.5pt,0 pt) -- ++(1pt,0 pt) ++(-0.5pt,-0.5pt) -- ++(0 pt,1pt);
\draw[color=ududff] (2.86,3.47) node {$H$};
\draw [color=ffqqqq] (4,2.5)-- ++(-1.5pt,-1.5pt) -- ++(3pt,3pt) ++(-3pt,0) -- ++(3pt,-3pt);
\draw[color=ffqqqq] (4.36,2.61) node {$I$};
\draw [color=ttzzqq] (2.4035955056179774,1.5022471910112358)-- ++(-1.5pt,-1.5pt) -- ++(3pt,3pt) ++(-3pt,0) -- ++(3pt,-3pt);
\draw[color=ttzzqq] (2.48,1.93) node {$J$};
\end{tikzpicture}};
\drawshadow{img}{black}
\end{tikzpicture}
\end{minipage}
\begin{minipage}{\dimexpr\linewidth-6cm}
On considère le cube ABCDEFGH ci-contre.

\medskip

Soit I le milieu de [GC], soit J le point défini par : $\vv{AJ} = x\vv{AI}$, où $0 \leqslant x \leqslant 1$, et soit $K$ le point défini par $\vv{EK}=\dfrac{2}{3}\vv{EH}$.
\end{minipage}
\begin{enumerate}
\item Exprimer $\vv{AI}$ en fonction de $\vv{AB}$, $\vv{AD}$ et $\vv{AE}$.
\item Exprimer $\vv{CJ}$ en fonction de $\vv{AB}$, $\vv{AD}$ et $\vv{AE}$.
\item Exprimer $\vv{KJ}$ en fonction de $\vv{AB}$, $\vv{AD}$ et $\vv{AE}$.
\item Exprimer $\vv{IK}$ en fonction de $\vv{AB}$, $\vv{AD}$ et $\vv{AE}$.
\end{enumerate}

