This exercise is a multiple choice questionnaire. For each question, only one of the three propositions is correct.

In all the following questions, space is referred to an orthonormal coordinate system.

\begin{enumerate}
  \item Consider the line $\Delta_1$ with parametric representation $\left\{ \begin{aligned} x &= 1 - 3t \\ y &= 4 + 2t \\ z &= t \end{aligned} \right.$, where $t \in \mathbb{R}$ as well as the line $\Delta_2$ with parametric representation $\left\{ \begin{aligned} x &= -4 + s \\ y &= 2 + 2s \\ z &= -1 + s \end{aligned} \right.$, where $s \in \mathbb{R}$.\\
a. The lines $\Delta_1$ and $\Delta_2$ are parallel.\\
b. The lines $\Delta_1$ and $\Delta_2$ are orthogonal.\\
c. The lines $\Delta_1$ and $\Delta_2$ are secant.
  \item Consider the line $d$ with parametric representation $\left\{ \begin{aligned} x &= 1 + t \\ y &= 3 - t \\ z &= 1 + 2t \end{aligned} \right.$, where $t \in \mathbb{R}$, and the plane $P$ with Cartesian equation: $4x + 2y - z + 3 = 0$.\\
a. The line $d$ is contained in the plane $P$.\\
b. The line $d$ is strictly parallel to the plane $P$.\\
c. The line $d$ is secant to the plane $P$.
  \item Consider the points $\mathrm{A}(3;2;1)$, $\mathrm{B}(7;3;1)$, $\mathrm{C}(-1;4;5)$ and $\mathrm{D}(-3;3;5)$.\\
a. The points $\mathrm{A}$, $\mathrm{B}$, $\mathrm{C}$ and D are not coplanar.\\
b. The points $\mathrm{A}$, $\mathrm{B}$ and C are collinear.\\
c. $\overrightarrow{\mathrm{AB}}$ and $\overrightarrow{\mathrm{CD}}$ are collinear.
  \item Consider the planes $Q$ and $Q'$ with respective Cartesian equations $3x - 2y + z + 1 = 0$ and $4x + y - z + 3 = 0$.\\
a. The point $\mathrm{R}(1;1;-2)$ belongs to both planes.\\
b. The two planes are orthogonal.\\
c. The two planes are secant with intersection the line with parametric representation
$$\left\{ \begin{aligned} x &= t \\ y &= 7t + 4, \text{ where } t \in \mathbb{R}. \\ z &= 11t + 7 \end{aligned} \right.$$
\end{enumerate}