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

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

\begin{enumerate}
  \item Consider the points $A(1; 0; 3)$ and $B(4; 1; 0)$.

A parametric representation of the line (AB) is:\\
a. $\left\{ \begin{aligned} x & = 3 + t \\ y & = 1 \\ z & = -3 + 3t \end{aligned} \right.$ with $t \in \mathbb{R}$\\
b. $\left\{ \begin{array}{l} x = 1 + 4t \\ y = 3 \\ z = 3 \end{array} \right.$ with $t \in \mathbb{R}$\\
c. $\left\{ \begin{aligned} x & = 1 + 3t \\ y & = t \\ z & = 3 - 3t \end{aligned} \right.$ with $t \in \mathbb{R}$\\
d. $\left\{ \begin{aligned} x & = 4 + t \\ y & = 1 \\ z & = 3 - 3t \end{aligned} \right.$ with $t \in \mathbb{R}$

  \item Consider the line (d) with parametric representation
$\left\{ \begin{aligned} x & = 3 + 4t \\ y & = 6t \\ z & = 4 - 2t \end{aligned} \right.$ with $t \in \mathbb{R}$

Among the following points, which one belongs to the line (d)?\\
a. $M(7; 6; 6)$\\
b. $N(3; 6; 4)$\\
c. $P(4; 6; -2)$\\
d. $R(-3; -9; 7)$

  \item Consider the line $(d')$ with parametric representation
$\left\{ \begin{aligned} x & = -2 + 3k \\ y & = -1 - 2k \\ z & = 1 + k \end{aligned} \right.$ with $k \in \mathbb{R}$

The lines $(d)$ and $(d')$ are:\\
a. secant\\
b. non-coplanar\\
c. parallel\\
d. coincident

  \item Consider the plane $(P)$ passing through the point $I(2; 1; 0)$ and perpendicular to the line (d).

An equation of the plane $(P)$ is:\\
a. $2x + 3y - z - 7 = 0$\\
b. $-x + y - 4z + 1 = 0$\\
c. $4x + 6y - 2z + 9 = 0$\\
d. $2x + y + 1 = 0$
\end{enumerate}