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.

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

We consider:
\begin{itemize}
  \item the points $A(-1; -2; 3)$, $B(1; -2; 7)$ and $C(1; 0; 2)$;
  \item the line $\Delta$ with parametric representation: $\left\{\begin{array}{l} x = 1 - t \\ y = 2 \\ z = -4 + 3t \end{array}\right.$, where $t \in \mathbb{R}$;
  \item the plane $\mathscr{P}$ with Cartesian equation: $3x + 2y + z - 4 = 0$;
  \item the plane $\mathscr{Q}$ with Cartesian equation: $-6x - 4y - 2z + 7 = 0$.
\end{itemize}

\begin{enumerate}
  \item Which of the following points belongs to the plane $\mathscr{P}$?\\
  a. $R(1; -3; 1)$;\\
  b. $S(1; 2; -1)$;\\
  c. $T(1; 0; 1)$;\\
  d. $U(2; -1; 1)$.
  \item Triangle ABC is:\\
  a. equilateral;\\
  b. right isosceles;\\
  c. isosceles non-right;\\
  d. right non-isosceles.
  \item The line $\Delta$ is:\\
  a. orthogonal to the plane $\mathscr{P}$;\\
  b. secant to the plane $\mathscr{P}$;\\
  c. included in the plane $\mathscr{P}$;\\
  d. strictly parallel to the plane $\mathscr{P}$.
  \item We are given the dot product $\overrightarrow{BA} \cdot \overrightarrow{BC} = 20$.\\
  A measure to the nearest degree of the angle $\widehat{ABC}$ is:\\
  a. $34°$;\\
  b. $120°$;\\
  c. $90°$;\\
  d. $0°$.
  \item The intersection of planes $\mathscr{P}$ and $\mathscr{Q}$ is:\\
  a. a plane;\\
  b. the empty set;\\
  c. a line;\\
  d. reduced to a point.
\end{enumerate}