This exercise is a multiple choice questionnaire. For each of the following questions, only one of the four proposed answers is correct.\\
A correct answer earns one point. An incorrect answer, a multiple answer, or the absence of an answer to a question earns neither points nor deducts points.\\
To answer, indicate on your paper the question number and the letter of the chosen answer. No justification is required.

SABCD is a regular pyramid with square base ABCD in which all edges have the same length.\\
The point I is the center of the square ABCD.\\
We assume that: $\mathrm{IC} = \mathrm{IB} = \mathrm{IS} = 1$.\\
The points K, L and M are the midpoints of edges [SD], [SC] and [SB] respectively.

\begin{enumerate}
  \item The following lines are not coplanar:\\
a. (DK) and (SD)\\
b. (AS) and (IC)\\
c. (AC) and (SB)\\
d. (LM) and (AD)
\end{enumerate}

For the following questions, we place ourselves in the orthonormal coordinate system of space $(\mathrm{I}; \overrightarrow{\mathrm{IC}}, \overrightarrow{\mathrm{IB}}, \overrightarrow{\mathrm{IS}})$. In this coordinate system, we are given the coordinates of the following points:
$$\mathrm{I}(0;0;0) \quad ; \quad \mathrm{A}(-1;0;0) \quad ; \quad \mathrm{B}(0;1;0) \quad ; \quad \mathrm{C}(1;0;0) \quad ; \quad \mathrm{D}(0;-1;0) \quad ; \quad \mathrm{S}(0;0;1).$$

\begin{enumerate}
  \setcounter{enumi}{1}
  \item The coordinates of the midpoint N of [KL] are:\\
a. $\left(\frac{1}{4};\frac{1}{4};\frac{1}{4}\right)$\\
b. $\left(\frac{1}{4};-\frac{1}{4};\frac{1}{2}\right)$\\
c. $\left(-\frac{1}{4};\frac{1}{4};\frac{1}{2}\right)$\\
d. $\left(-\frac{1}{2};\frac{1}{2};1\right)$
  \item The coordinates of the vector $\overrightarrow{\mathrm{AS}}$ are:\\
a. $\left(\begin{array}{l}1\\1\\0\end{array}\right)$\\
b. $\left(\begin{array}{l}1\\0\\1\end{array}\right)$\\
c. $\left(\begin{array}{c}2\\1\\-1\end{array}\right)$\\
d. $\left(\begin{array}{l}1\\1\\1\end{array}\right)$
  \item A parametric representation of the line (AS) is:\\
a. $\left\{\begin{array}{rl}x &= -1-t\\y &= t\\z &= -t\end{array}\right.$\\
b. $\left\{\begin{aligned}x =& -1+2t\\y =& 0\\z =& 1+2t\end{aligned}\right.$\\
c. $\left\{\begin{aligned}x &= t\\y &= 0\\z &= 1+t\end{aligned}\right.$\\
d. $\left\{\begin{aligned}x &= -1-t\\y &= 1+t\\z &= 1-t\end{aligned}\right. (t \in \mathbb{R})$
  \item A Cartesian equation of the plane (SCB) is:\\
a. $y+z-1=0$\\
b. $x+y+z-1=0$\\
c. $x-y+z=0$\\
d. $x+z-1=0$
\end{enumerate}