For each of the following statements, indicate whether it is true or false. Each answer must be justified. An unjustified answer earns no points.\\
Space is referred to an orthonormal coordinate system $(\mathrm{O}; \vec{\imath}, \vec{\jmath}, \vec{k})$.\\
We consider the line $(d)$ whose parametric representation is:
$$\left\{\begin{array}{rl}
x & = 3 - 2t \\
y & = -1 \\
z & = 2 - 6t
\end{array}, \text{ where } t \in \mathbb{R}\right.$$
We also consider the following points:
\begin{itemize}
  \item $\mathrm{A}(3; -3; -2)$
  \item $\mathrm{B}(5; -4; -1)$
  \item C the point on line $(d)$ with x-coordinate 2
  \item H the orthogonal projection of point B onto the plane $\mathscr{P}$ with equation $x + 3z - 7 = 0$
\end{itemize}

\textbf{Statement 1:} The line $(d)$ and the y-axis are two non-coplanar lines.

\textbf{Statement 2:} The plane passing through $A$ and perpendicular to line $(d)$ has the Cartesian equation:
$$x + 3z + 3 = 0$$

\textbf{Statement 3:} A measure, expressed in radians, of the geometric angle $\widehat{\mathrm{BAC}}$ is $\frac{\pi}{6}$.

\textbf{Statement 4:} The distance BH is equal to $\frac{\sqrt{10}}{2}$.