9000101101
Level:
B
Find the distance from the point \(A = [0;1;-3]\)
to the point \(B = [-1;3;0]\).
\(\sqrt{14}\)
\(3\)
\(4\)
\(\sqrt{26}\)
Analytical Space Geometry
9000101102
Level:
B
Find the distance between the point \(A = [1;0;1]\)
and the line \(p\).
\[
\begin{aligned}p\colon x& = 2, &
\\y & = 3t,
\\z & = 1 - t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(1\)
\(0\)
\(2\)
\(3\)
9000101103
Level:
B
Find the distance between two parallel lines
\(p\) and
\(q\).
\[
\begin{aligned}p\colon x& = 2, &
\\y & = 3t,
\\z & = 1 - t;\ t\in \mathbb{R}
\\ \end{aligned}\qquad \qquad \begin{aligned}q\colon x& = 3, &
\\y & = 6s,
\\z & = 1 - 2s;\ s\in \mathbb{R}
\\ \end{aligned}
\]
\(1\)
\(2\)
\(3\)
\(4\)
9000101104
Level:
B
Find the distance between the point \(A = [-1;1;0]\)
and the plane \(\alpha \).
\[
\alpha \colon 12y + 5z - 2 = 0
\]
\(\frac{10}
{13}\)
\(\frac{15}
{13}\)
\(\frac{17}
{13}\)
\(\frac{14}
{13}\)
9000101107
Level:
B
Find the distance between the line \(p\)
and the plane \(\alpha \).
\[
\alpha \colon x-3y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] p\colon x& = 1 + t, &
\\y & = -3t,
\\z & = 2;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(0\)
\(\frac{5}
{\sqrt{17}}\)
\(2\)
\(1\)
9000101109
Level:
B
The points \(A = [0;5;0]\),
\(B = [5;5;0]\),
\(C = [5;0;0]\),
\(D = [0;0;0]\) define a cube
\(ABCDEFGH\). Find the distance
between the line \(AB\)
and the plane \(EFG\).
\(5\)
\(3\)
\(4\)
\(6\)
9000101110
Level:
B
The points \(A = [0;5;0]\),
\(B = [5;5;0]\),
\(C = [5;0;0]\),
\(D = [0;0;0]\) define a cube
\(ABCDEFGH\). Find the distance
between the point \(A\)
and the point \(F\).
\(\sqrt{50}\)
\(\sqrt{5}\)
\(5\)
\(10\)
9000101108
Level:
B
Find the distance between the line \(q\)
and the plane \(\beta \).
\[
\beta \colon x+4y+2z-4 = 0,\qquad \qquad \begin{aligned}[t] q\colon x& = 4, &
\\y & = -2t,
\\z & = 1 + 4t;\ t\in \mathbb{R}
\\ \end{aligned}
\]
\(\frac{2}
{\sqrt{21}}\)
\(\frac{4}
{\sqrt{21}}\)
\(0\)
\(1\)
9000101009
Level:
A
Determine whether the following two lines are identical, parallel, intersecting or
skew.
\[\begin{aligned}
a\colon x & = t, & &
\\y & = -t, & &
\\z & = 1 - t;\ t\in \mathbb{R} & &
\end{aligned}\]\[\begin{aligned}
b\colon x & = -s, & &
\\y & = s, & &
\\z & = 1 + s;\ s\in \mathbb{R} & &
\end{aligned}\]
identical lines
skew lines
intersecting lines
parallel, not identical lines