For each of the following statements, indicate whether it is true or false.\\
Each answer must be justified. An unjustified answer earns no points. In this exercise, the questions are independent of one another.\\
The four statements are placed in the following situation:\\
In space equipped with an orthonormal reference frame ( $\mathrm { O } ; \vec { \imath } , \vec { \jmath } , \vec { k }$ ), we consider the points:

$$\mathrm { A } ( 2 ; 1 ; - 1 ) , \quad \mathrm { B } ( - 1 ; 2 ; 1 ) \text { and } \quad \mathrm { C } ( 5 ; 0 ; - 3 ) .$$

We denote $\mathscr { P }$ the plane with Cartesian equation:

$$x + 5 y - 2 z + 3 = 0 .$$

We denote $\mathscr { D }$ the line with parametric representation:

$$\left\{ \begin{array} { r l } 
x & = - t + 3 \\
y & = t + 2 \\
z & = 2 t + 1
\end{array} , t \in \mathbb { R } . \right.$$

\textbf{Statement 1:}\\
The vector $\vec { n } \left( \begin{array} { l } 1 \\ 0 \\ 2 \end{array} \right)$ is normal to the plane (OAC).

\textbf{Statement 2:}\\
The lines $\mathscr { D }$ and ( AB ) intersect at point C .

\textbf{Statement 3:}\\
The line $\mathscr { D }$ is parallel to the plane $\mathscr { P }$.

\textbf{Statement 4:}\\
The perpendicular bisector plane of segment $[ \mathrm { BC } ]$, denoted $Q$, has Cartesian equation:

$$3 x - y - 2 z - 7 = 0 .$$

Recall that the perpendicular bisector plane of a segment is the plane perpendicular to this segment and passing through its midpoint.