In space with an orthonormal coordinate system, we consider
\begin{itemize}
  \item the points $\mathrm{A}(12;0;0), \mathrm{B}(0;-15;0), \mathrm{C}(0;0;20), \mathrm{D}(2;7;-6), \mathrm{E}(7;3;-3)$;
  \item the plane $\mathscr{P}$ with Cartesian equation: $2x + y - 2z - 5 = 0$
\end{itemize}

For each of the following statements, indicate whether it is true or false by justifying your answer. An unjustified answer will not be taken into account.

\textbf{Statement 1}\\
A Cartesian equation of the plane parallel to $\mathscr{P}$ and passing through point A is:
$$2x + y + 2z - 24 = 0$$

\textbf{Statement 2}\\
A parametric representation of line (AC) is: $\left\{ \begin{array}{rl} x &= 9 - 3t \\ y &= 0 \\ z &= 5 + 5t \end{array}, t \in \mathbb{R} \right.$.

\textbf{Statement 3}\\
Line (DE) and plane $\mathscr{P}$ have at least one point in common.

\textbf{Statement 4}\\
Line (DE) is orthogonal to plane (ABC).