For each of the following statements, indicate whether it is true or false and justify the answer.

Space is equipped with an orthonormal coordinate system $(\mathrm{O}, \vec{\imath}, \vec{\jmath}, \vec{k})$. The points $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ are defined by their coordinates:
$$\mathrm{A}(3; -1; 4), \quad \mathrm{B}(-1; 2; -3), \quad \mathrm{C}(4; -1; 2).$$
The plane $\mathscr{P}$ has the Cartesian equation: $2x - 3y + 2z - 7 = 0$.\\
The line $\Delta$ has the parametric representation $\left\{\begin{array}{rl} x &= -1 + 4t \\ y &= 4 - t \\ z &= -8 + 2t \end{array}, t \in \mathbb{R}\right.$.

\textbf{Statement 1:} The lines $\Delta$ and $(AC)$ are orthogonal.

\textbf{Statement 2:} The points $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ determine a plane and this plane has the Cartesian equation $2x + 5y + z - 5 = 0$.

\textbf{Statement 3:} All points whose coordinates $(x; y; z)$ are given by
$$\left\{\begin{array}{rl} x &= 1 + s - 2s' \\ y &= 1 - 2s + s' \\ z &= 1 - 4s + 2s' \end{array}\right., \quad s, s' \in \mathbb{R}$$
lie in the plane $\mathscr{P}$.

\textbf{Statement 4:} There exists a plane parallel to the plane $\mathscr{P}$ which contains the line $\Delta$.