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 neither awards nor deducts points.\\
The five questions are independent.\\
Space is equipped with an orthonormal reference frame $(\mathrm{O}; \vec{\imath}, \vec{\jmath}, \vec{k})$.\\
We consider the points $\mathrm{A}(-1; 2; 5)$, $\mathrm{B}(3; 6; 3)$, $\mathrm{C}(3; 0; 9)$ and $\mathrm{D}(8; -3; -8)$.\\
We admit that points $\mathrm{A}$, $\mathrm{B}$ and $\mathrm{C}$ are not collinear.

\begin{enumerate}
  \item Triangle ABC is:\\
a. isosceles right-angled at A\\
b. isosceles right-angled at B\\
c. isosceles right-angled at C\\
d. equilateral

  \item A Cartesian equation of plane (BCD) is:\\
a. $2x + y + z - 15 = 0$\\
b. $9x - 5y + 3 = 0$\\
c. $4x + y + z - 21 = 0$\\
d. $11x + 5z - 73 = 0$

  \item We admit that plane $(\mathrm{ABC})$ has Cartesian equation $x - 2y - 2z + 15 = 0$.\\
We call H the orthogonal projection of point D onto plane (ABC).\\
We can affirm that:\\
a. $\mathrm{H}(-2; 17; 12)$\\
b. $\mathrm{H}(3; 7; 2)$\\
c. $\mathrm{H}(3; 2; 7)$\\
d. $\mathrm{H}(-15; 1; -1)$

  \item Let the line $\Delta$ with parametric representation $\left\{\begin{array}{l} x = 5 + t \\ y = 3 - t \\ z = -1 + 3t \end{array}\right.$, with $t$ real.\\
Lines (BC) and $\Delta$ are:\\
a. coincident\\
b. strictly parallel\\
c. intersecting\\
d. non-coplanar

  \item We consider the plane $\mathscr{P}$ with Cartesian equation $2x - y + 2z - 6 = 0$.\\
We admit that plane (ABC) has Cartesian equation $x - 2y - 2z + 15 = 0$.\\
We can affirm that:\\
a. planes $\mathscr{P}$ and (ABC) are strictly parallel\\
b. planes $\mathscr{P}$ and (ABC) are intersecting and their intersection is line (AB)\\
c. planes $\mathscr{P}$ and (ABC) are intersecting and their intersection is line (AC)\\
d. planes $\mathscr{P}$ and (ABC) are intersecting and their intersection is line (BC)
\end{enumerate}