The figure below represents a cube ABCDEFGH. The three points I, J, K are defined by the following conditions:
\begin{itemize}
  \item I is the midpoint of segment [AD];
  \item J is such that $\overrightarrow{\mathrm{AJ}} = \frac{3}{4}\overrightarrow{\mathrm{AE}}$;
  \item K is the midpoint of segment [FG].
\end{itemize}
We place ourselves in the orthonormal coordinate system $(\mathrm{A}; \overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{AE}})$.
\begin{enumerate}
  \item a. Give without justification the coordinates of points I, J and K.\\
b. Determine the real numbers $a$ and $b$ such that the vector $\vec{n}(4; a; b)$ is orthogonal to the vectors $\overrightarrow{\mathrm{IJ}}$ and $\overrightarrow{\mathrm{IK}}$.\\
c. Deduce that a Cartesian equation of the plane (IJK) is: $4x - 6y - 4z + 3 = 0$.
  \item a. Give a parametric representation of the line (CG).\\
b. Calculate the coordinates of point N, the intersection of the plane (IJK) and the line (CG).\\
c. Place point N on the figure and construct in colour the cross-section of the cube by the plane (IJK).
\end{enumerate}