9000121703
Level:
A
Consider a triangle \(ABC\) with
sides of the lengths \(4\, \mathrm{cm}\),
\(4\, \mathrm{cm}\) and
\(4\, \mathrm{cm}\). Identify the type
of the triangle \(ABC\).
equilateral
right
obtuse
A
9000121007
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(S_{BE}S_{AH}\)
and \(HC\), where
\(S_{BE}\) and
\(S_{AH}\) are centers of
the segments \(BE\)
and \(AH\),
respectively.
\(60^{\circ }\)
\(26.57^{\circ }\)
\(45^{\circ }\)
\(53.13^{\circ }\)
9000121009
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(S_{HD}S_{FC}\)
and \(AB\), where
the points \(S_{HD}\)
and \(S_{FC}\) are
centers of \(HD\)
and \(FC\),
respectively.
\(26.57^{\circ }\)
\(45^{\circ }\)
\(54.74^{\circ }\)
\(60^{\circ }\)
9000121010
Level:
A
In the cube \(ABCDEFGH\) find the
angle between the lines \(ES_{CG}\)
and \(AG\), where
\(S_{CG}\) is the center
of the \(CG\).
\(54.74^{\circ }\)
\(19.47^{\circ }\)
\(35.26^{\circ }\)
\(60^{\circ }\)
9000107502
Level:
A
In the following list identify a line which is perpendicular to the line
\(q\).
\[
\begin{aligned}q\colon x& = 5 - t,&
\\y & = 3t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(p\colon x - 3y - 7 = 0\)
\(p\colon - x - 3y + 11 = 0\)
\(p\colon 3x - y = 0\)
\(p\colon y = 5\)
9000107510
Level:
A
In the following list identify a line parallel to the line
\(q\).
\[
\begin{aligned}q\colon x& = t, &
\\y & = 1 + 5t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(p\colon - 5x + y - 13 = 0\)
\(p\colon x + 5y - 1 = 0\)
\(p\colon x - 5 = 0\)
\(p\colon 10x + 2y - 1 = 0\)
9000107503
Level:
A
Among the lines in the following list (slope-intercept form) identify a line perpendicular
to the line
\[
y = \frac{3}{4}x + 1.
\]
\(y = -\frac{4}
{3}x - 2\)
\(y = -\frac{3}
{4}x - 1\)
\(y = \frac{4}
{3}x - 5\)
\(y = 3\)
9000106802
Level:
A
Find the normal vector of the line passing through the point
\(A = [3,-1]\) and
\(B = [2,2]\).
\((3,1)\)
\((-1,3)\)
\((1,-3)\)
\((1,3)\)
9000106803
Level:
A
Find the vector in the direction of the following line.
\[
p\colon y = \frac{2}
{3}x - 3
\]
\((3,2)\)
\(\left (\frac{2}
{3},-1\right )\)
\((3,-1)\)
\(\left (\frac{2}
{3},1\right )\)
9000106804
Level:
A
Find the normal vector of the following line.
\[
p\colon \begin{aligned}[t] x =&1 - 6t, &
\\y =& - 2 + 3t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\((1,2)\)
\((-6,3)\)
\((1,-2)\)
\((2,1)\)