9000106008
Level:
A
In the following list identify a normal vector of the following line.
\[
x - 2y - 10 = 0
\]
\(\left (1;-2\right )\)
\(\left (1;2\right )\)
\(\left (2;10\right )\)
\(\left (-2;-10\right )\)
Analytical plane geometry
9000106201
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{alignedat}{80}
p\colon x & = 1 + 2t, & &\phantom{t\in \mathbb{R}} & & & &
\\y & = 3 - 4t;\ & &t\in \mathbb{R} & & & &
\\\end{alignedat}\]
\((1;-2)\)
\((1;3)\)
\((3;1)\)
\((2;3)\)
9000106202
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{aligned}
x & = 1 - t, \\
y & = t;\ t\in \mathbb{R}
\\\end{aligned}\]
\((1;-1)\)
\((0;0)\)
\((1;0)\)
\((1;1)\)
9000106203
Level:
A
In the following list identify a vector having the same direction as the parametric
line \(p\).
\[ \begin{aligned}
p\colon x & = -5, \\
y & = 5t;\ t\in \mathbb{R}
\end{aligned}\]
\((0;1)\)
\((5;5)\)
\((5;0)\)
\((-5;5)\)
9000090910
Level:
C
Given lines \(p\)
and \(q\), find
\(m\in \mathbb{R}\) such that
the line \(p\) is
parallel to \(q\).
\[
p\colon x+4y-3 = 0,\qquad \begin{aligned}[t] q\colon x& = 1 + mt,&
\\y & = 2 - 3t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(m = 12\)
\(m = -\frac{1}
{12}\)
\(m = 4\)
\(m = \frac{5}
{2}\)
\(m = -1\)
9000090903
Level:
C
Given the line
\[
p\colon 3x - 2y + 11 = 0,
\]
find \(m\in \mathbb{R}\) such that
the point \(C = [m;0]\)
is on the line \(p\).
\(m = -\frac{11}
{3} \)
\(m = -1\)
\(m = 11\)
\(m = -\frac{1}
{11}\)
\(m = 2\)
9000090902
Level:
C
Given the parametric line \(p\),
find \(m\in \mathbb{R}\) such that
the point \(C = [m;3]\)
is on the line \(p\).
\[
\begin{aligned}p\colon x& = 1 - t, &
\\y & = -3 + 2t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(m = -2\)
\(m = 4\)
\(m = 11\)
\(m = -\frac{11}
{3} \)
\(m = \frac{3}
{2}\)
9000090901
Level:
C
Given two points \(A = [2;5]\)
and \(B = [-3;2]\), identify a
number \(m\in \mathbb{R}\) such
that the point \(C = [1;m]\)
is on the line \(AB\).
\(m = \frac{22}
{5} \)
\(m = 20\)
\(m = -3\)
\(m = \frac{2}
{3}\)
\(m = -\frac{5}
{2}\)
9000090904
Level:
C
Given lines \(p\)
and \(q\), find
\(m\in \mathbb{R}\) such that
the lines \(p\)
and \(q\)
are parallel.
\[
p\colon x - 2y + 7 = 0,\qquad q\colon mx + 3y - 11 = 0
\]
\(m = -\frac{3}
{2}\)
\(m = \frac{2}
{3}\)
\(m = \frac{3}
{2}\)
\(m = -\frac{2}
{3}\)
another solution
9000090905
Level:
C
Given lines \(p\)
and \(q\), find
\(m\in \mathbb{R}\) such that
the lines \(p\)
and \(q\)
are parallel.
\[
p\colon x - 2y + 7 = 0,\qquad q\colon x + 3y + m = 0
\]
does not exist
\(m = -7\)
\(m = -\frac{2}
{7}\)
\(m = 2\)
\(m = 7\)