Space is equipped with an orthonormal coordinate system $(O; \vec{\imath}, \vec{\jmath}, \vec{k})$ in which we consider:
\begin{itemize}
  \item the points $A(6; -6; 6)$, $B(-6; 0; 6)$ and $C(-2; -2; 11)$.
  \item the line $(d)$ orthogonal to the two secant lines $(AB)$ and $(BC)$ and passing through point A;
  \item the line $(d')$ with parametric representation:
\end{itemize}
$$\left\{\begin{aligned}
x &= -6 - 8t \\
y &= 4t, \text{ with } t \in \mathbb{R}. \\
z &= 6 + 5t
\end{aligned}\right.$$

This exercise is a multiple choice questionnaire. For each of the following questions, only one of the four proposed answers is correct. A wrong answer, multiple answers or absence of answer to a question neither awards nor deducts points. No justification is required.

\textbf{Question 1}\\
Among the following vectors, which is a direction vector of the line $(d)$?\\
a. $\overrightarrow{u_1}\left(\begin{array}{c}-6 \\ 3 \\ 0\end{array}\right)$\\
b. $\overrightarrow{u_2}\left(\begin{array}{l}1 \\ 2 \\ 6\end{array}\right)$\\
c. $\overrightarrow{u_3}\left(\begin{array}{c}1 \\ 2 \\ 0.2\end{array}\right)$\\
d. $\overrightarrow{u_4}\left(\begin{array}{l}1 \\ 2 \\ 0\end{array}\right)$

\textbf{Question 2}\\
Among the following equations, which is a parametric representation of the line (AB)?\\
a. $\left\{\begin{aligned}x &= 2t + 6 \\ y &= -6 \text{ with } t \in \mathbb{R} \\ z &= t + 6\end{aligned}\right.$\\
b. $\left\{\begin{aligned}x &= 2t - 6 \\ y &= -6 \text{ with } t \in \mathbb{R} \\ z &= -t - 6\end{aligned}\right.$\\
c. $\left\{\begin{aligned}x &= 2t + 6 \\ y &= -t - 6 \text{ with } t \in \mathbb{R} \\ z &= 6\end{aligned}\right.$\\
d. $\left\{\begin{aligned}x &= 2t + 6 \\ y &= t - 6 \text{ with } t \in \mathbb{R} \\ z &= 6\end{aligned}\right.$

\textbf{Question 3}\\
A direction vector of the line $(d')$ is:\\
a. $\overrightarrow{v_1}\left(\begin{array}{c}-6 \\ 0 \\ 6\end{array}\right)$\\
b. $\overrightarrow{v_2}\left(\begin{array}{c}-14 \\ 4 \\ 11\end{array}\right)$\\
c. $\overrightarrow{v_3}\left(\begin{array}{c}8 \\ -4 \\ -5\end{array}\right)$\\
d. $\overrightarrow{v_4}\left(\begin{array}{l}8 \\ 4 \\ 5\end{array}\right)$

\textbf{Question 4}\\
Which of the following four points belongs to the line $(d')$?\\
a. $M_1(50; -28; -29)$\\
b. $M_2(-14; -4; 1)$\\
c. $M_3(2; -4; -1)$\\
d. $M_4(-3; 0; 3)$

\textbf{Question 5}\\
The plane with equation $x = 1$ has as normal vector:\\
a. $\overrightarrow{n_1}\left(\begin{array}{l}1 \\ 0 \\ 0\end{array}\right)$\\
b. $\overrightarrow{n_2}\left(\begin{array}{l}0 \\ 1 \\ 1\end{array}\right)$\\
c. $\overrightarrow{n_3}\left(\begin{array}{l}0 \\ 1 \\ 0\end{array}\right)$\\
d. $\overrightarrow{n_4}\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)$