9000106208
Level:
A
In the following list identify a normal vector to the line
\(p\).
\[
p\colon 2y - 1 = 0
\]
\((0,1)\)
\((2,0)\)
\((2,-1)\)
$(2,1)$
Analytical Plane Geometry
9000106003
Level:
A
In the following list identify a vector in the direction of the following parametric
line.
\[\begin{aligned}
x =\ &2, & &
\\y =\ &t,\ t\in \mathbb{R} & &
\end{aligned}\]
\(\left (0,1\right )\)
\(\left (2,1\right )\)
\(\left (2,0\right )\)
\(\left (1,0\right )\)
9000106209
Level:
A
In the following list find the vector having the same direction as the line
\(p\).
\[
p\colon y = 2x + 1
\]
\((1,2)\)
\((2,-1)\)
\((2,1)\)
\((1,-2)\)
9000106004
Level:
A
In the following list identify a vector in the direction of the following parametric
line.
\[\begin{aligned}
x =\ &t, & &
\\y =\ &1,\ t\in \mathbb{R}. & &
\end{aligned}\]
\(\left (1,0\right )\)
\(\left (0,0\right )\)
\(\left (0,1\right )\)
\(\left (1,1\right )\)
9000106210
Level:
A
In the following list find the vector having the same direction as the line
\(p\).
\[
p\colon 3x - 2y + 1 = 0
\]
\((2,3)\)
\((3,-2)\)
\((-2,1)\)
\((3,2)\)
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
\(m = -7\)
\(m = -\frac{2}
{7}\)
\(m = 2\)
\(m = 7\)
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
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 \(AB\).
\(m = \frac{22}
{5} \)
\(m = 20\)
\(m = -3\)
\(m = \frac{2}
{3}\)
\(m = -\frac{5}
{2}\)
9000090902
Level:
C
Given the parametric line \(p\),
find \(m\in \mathbb{R}\) such that
the point \(C = [m,3]\)
is on the line \(p\).
\[
\begin{aligned}p\colon x& = 1 - t, &
\\y & = -3 + 2t,\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(m = -2\)
\(m = 4\)
\(m = 11\)
\(m = -\frac{11}
{3} \)
\(m = \frac{3}
{2}\)
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 \(p\).
\(m = -\frac{11}
{3} \)
\(m = -1\)
\(m = 11\)
\(m = -\frac{1}
{11}\)
\(m = 2\)