This exercise is a multiple choice questionnaire. No justification is required. For each question, only one of the four propositions is correct. Each correct answer earns one point. An incorrect answer or no answer does not deduct any points.
In an orthonormal coordinate system in space, consider the points $\mathrm { A } ( 2 ; 5 ; - 1 ) , \mathrm { B } ( 3 ; 2 ; 1 )$ and $\mathrm { C } ( 1 ; 3 ; - 2 )$. Triangle ABC is: a. right-angled and not isosceles b. isosceles and not right-angled c. right-angled and isosceles d. equilateral
In an orthonormal coordinate system in space, consider the plane $P$ with equation $2 x - y + 3 z - 1 = 0$ and the point $\mathrm { A } ( 2 ; 5 ; - 1 )$. A parametric representation of the line $d$, perpendicular to plane $P$ and passing through A is: a. $\left\{ \begin{aligned} x & = 2 + 2 t \\ y & = 5 + t \\ z & = - 1 + 3 t \end{aligned} \right.$ b. $\left\{ \begin{aligned} x & = 2 + 2 t \\ y & = - 1 + 5 t \\ z & = 3 - t \end{aligned} \right.$ c. $\left\{ \begin{aligned} x & = 6 - 2 t \\ y & = 3 + t \\ z & = 5 - 3 t \end{aligned} \right.$ d. $\left\{ \begin{aligned} x & = 1 + 2 t \\ y & = 4 - t \\ z & = - 2 + 3 t \end{aligned} \right.$
Let A and B be two distinct points in the plane. The set of points $M$ in the plane such that $\overrightarrow { M A } \cdot \overrightarrow { M B } = 0$ is: a. the empty set b. the perpendicular bisector of segment [AB] c. the circle with diameter $[ \mathrm { AB } ]$ d. the line (AB)
The figure below represents a cube ABCDEFGH. Points I and J are the midpoints of edges $[ \mathrm { GH } ]$ and $[ \mathrm { FG } ]$ respectively. Points M and N are the centres of faces ABFE and BCGF respectively. Lines (IJ) and (MN) are: a. perpendicular b. intersecting, non-perpendicular c. orthogonal d. parallel
This exercise is a multiple choice questionnaire. No justification is required. For each question, only one of the four propositions is correct. Each correct answer earns one point. An incorrect answer or no answer does not deduct any points.
\begin{enumerate}
\item In an orthonormal coordinate system in space, consider the points $\mathrm { A } ( 2 ; 5 ; - 1 ) , \mathrm { B } ( 3 ; 2 ; 1 )$ and $\mathrm { C } ( 1 ; 3 ; - 2 )$. Triangle ABC is:\\
a. right-angled and not isosceles\\
b. isosceles and not right-angled\\
c. right-angled and isosceles\\
d. equilateral
\item In an orthonormal coordinate system in space, consider the plane $P$ with equation $2 x - y + 3 z - 1 = 0$ and the point $\mathrm { A } ( 2 ; 5 ; - 1 )$. A parametric representation of the line $d$, perpendicular to plane $P$ and passing through A is:\\
a. $\left\{ \begin{aligned} x & = 2 + 2 t \\ y & = 5 + t \\ z & = - 1 + 3 t \end{aligned} \right.$ b. $\left\{ \begin{aligned} x & = 2 + 2 t \\ y & = - 1 + 5 t \\ z & = 3 - t \end{aligned} \right.$ c. $\left\{ \begin{aligned} x & = 6 - 2 t \\ y & = 3 + t \\ z & = 5 - 3 t \end{aligned} \right.$ d. $\left\{ \begin{aligned} x & = 1 + 2 t \\ y & = 4 - t \\ z & = - 2 + 3 t \end{aligned} \right.$
\item Let A and B be two distinct points in the plane. The set of points $M$ in the plane such that $\overrightarrow { M A } \cdot \overrightarrow { M B } = 0$ is:\\
a. the empty set\\
b. the perpendicular bisector of segment [AB]\\
c. the circle with diameter $[ \mathrm { AB } ]$\\
d. the line (AB)
\item The figure below represents a cube ABCDEFGH. Points I and J are the midpoints of edges $[ \mathrm { GH } ]$ and $[ \mathrm { FG } ]$ respectively. Points M and N are the centres of faces ABFE and BCGF respectively.\\
Lines (IJ) and (MN) are:\\
a. perpendicular\\
b. intersecting, non-perpendicular\\
c. orthogonal\\
d. parallel
\end{enumerate}