Space is referred to an orthonormal coordinate system $( O ; \vec { \imath } , \vec { \jmath } , \vec { k } )$.
We consider:

\begin{itemize}
  \item the points $C ( 3 ; 0 ; 0 )$, $D ( 0 ; 2 ; 0 )$, $H ( - 6 ; 2 ; 2 )$ and $J \left( \frac { - 54 } { 13 } ; \frac { 62 } { 13 } ; 0 \right)$;
  \item the plane $P$ with Cartesian equation $2 x + 3 y + 6 z - 6 = 0$;
  \item the plane $P ^ { \prime }$ with Cartesian equation $x - 2 y + 3 z - 3 = 0$;
  \item the line $( d )$ with a parametric representation: $\left\{ \begin{array} { l } x = - 8 + \frac { 1 } { 3 } t \\ y = - 1 + \frac { 1 } { 2 } t \\ z = - 4 + t \end{array} , t \in \mathbf { R } \right.$
\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.

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

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

Statement 3: The planes $P$ and $P ^ { \prime }$ are secant and their intersection is the line $\Delta$

$$\text { with a parametric representation: } \left\{ \begin{array} { l } 
x = 3 - 3 t \\
y = 0 \\
z = t
\end{array} , t \in \mathbf { R } \right. \text {. }$$

Statement 4: The point $J$ is the orthogonal projection of the point $H$ onto the line ( $C D$ ).