Space is referred to an orthonormal coordinate system $(\mathrm{O}; \vec{\imath}, \vec{\jmath}, \vec{k})$.\\
We consider:
\begin{itemize}
  \item the points $\mathrm{C}(3; 0; 0)$, $\mathrm{D}(0; 2; 0)$, $\mathrm{H}(-6; 2; 2)$ and $\mathrm{J}\left(\frac{-54}{13}; \frac{62}{13}; 0\right)$;
  \item the plane $P$ with Cartesian equation $2x + 3y + 6z - 6 = 0$;
  \item the plane $P'$ with Cartesian equation $x - 2y + 3z - 3 = 0$;
  \item the line $(d)$ with a parametric representation: $\left\{\begin{array}{l} x = -8 + \frac{1}{3}t \\ y = -1 + \frac{1}{2}t \\ z = -4 + t \end{array}, t \in \mathbb{R}\right.$
\end{itemize}
For each of the following statements, specify whether it is true or false, then justify the answer given. An answer without justification will not be taken into account.

\textbf{Statement 1:} The line $(d)$ is orthogonal to the plane $P$ and intersects this plane at $H$.

\textbf{Statement 2:} The measure in degrees of the angle $\widehat{\mathrm{DCH}}$, rounded to $10^{-1}$, is $17.3^{\circ}$.

\textbf{Statement 3:} The planes $P$ and $P'$ are secant and their intersection is the line $\Delta$ with a parametric representation: $\left\{\begin{array}{l} x = 3 - 3t \\ y = 0 \\ z = t \end{array}, t \in \mathbb{R}\right.$.

\textbf{Statement 4:} Point J is the orthogonal projection of point H onto the line (CD).