For each of the following statements, indicate whether it is true or false. Justify each answer. An unjustified answer earns no points.

We equip space with an orthonormal coordinate system ( $\mathrm { O } ; \vec { \imath } , \vec { \jmath } , \vec { k }$ ).

\begin{enumerate}
  \item We consider the points $\mathrm { A } ( - 1 ; 0 ; 5 )$ and $\mathrm { B } ( 3 ; 2 ; - 1 )$.

  Statement 1: A parametric representation of the line (AB) is
  $$\left\{ \begin{aligned} x & = 3 - 2 t \\ y & = 2 - t \text { with } t \in \mathbb { R } \\ z & = - 1 + 3 t \end{aligned} \right.$$

  Statement 2: The vector $\vec { n } \left( \begin{array} { c } 5 \\ - 2 \\ 1 \end{array} \right)$ is normal to the plane (OAB).

  \item We consider:
  \begin{itemize}
    \item the line $d$ with parametric representation $\left\{ \begin{aligned} x & = 15 + k \\ y & = 8 - k \\ z & = - 6 + 2 k \end{aligned} \right.$ with $k \in \mathbb { R }$;
    \item the line $d ^ { \prime }$ with parametric representation $\left\{ \begin{array} { l } x = 1 + 4 s \\ y = 2 + 4 s \\ z = 1 - 6 s \end{array} \right.$ with $s \in \mathbb { R }$.
  \end{itemize}

  Statement 3: The lines $d$ and $d ^ { \prime }$ are not coplanar.

  \item We consider the plane $\mathscr { P }$ with equation $x - y + z + 1 = 0$.

  Statement 4: The distance from point $\mathrm { C } ( 2 ; - 1 ; 2 )$ to the plane $\mathscr { P }$ is equal to $2 \sqrt { 3 }$.
\end{enumerate}