Space geometry

9000101103

Level:

Find the distance between two parallel lines

p

and

q

\begin{aligned} p : x & = 2, \\ y & = 3 t, \\ z & = 1 - t; t \in R \end{aligned} \begin{aligned} q : x & = 3, \\ y & = 6 s, \\ z & = 1 - 2 s; s \in R \end{aligned}

1

2

3

4

9000101104

Level:

Find the distance between the point

A = [- 1; 1; 0]

and the plane

α

α : 12 y + 5 z - 2 = 0

\frac{10}{13}

\frac{15}{13}

\frac{17}{13}

\frac{14}{13}

9000101105

Level:

Find the distance between two parallel planes

α

and

β

\begin{aligned} α & : x - 1.5 y - 3 z - 1 = 0, \\ β & : 2 x - 3 y - 6 z + 3 = 0 \end{aligned}

\frac{5}{7}

\frac{1}{7}

\frac{2}{49}

\frac{2}{41}

9000101106

Level:

In the following list identify a point which does not have zero distance from the line

m

\begin{aligned} m : x & = s, \\ y & = 8 - s, \\ z & = 1 + 3 s; s \in R \end{aligned}

[2; 6; 10]

[0; 8; 1]

[1; 7; 4]

[8; 0; 25]

9000101107

Level:

Find the distance between the line

p

and the plane

α

α : x - 3 y + 2 z - 4 = 0, \begin{aligned} p : x & = 1 + t, \\ y & = - 3 t, \\ z & = 2; t \in R \end{aligned}

0

\frac{5}{\sqrt{17}}

2

1

9000101108

Level:

Find the distance between the line

q

and the plane

β

β : x + 4 y + 2 z - 4 = 0, \begin{aligned} q : x & = 4, \\ y & = - 2 t, \\ z & = 1 + 4 t; t \in R \end{aligned}

\frac{2}{\sqrt{21}}

\frac{4}{\sqrt{21}}

0

1

9000101109

Level:

The points

A = [0; 5; 0]

B = [5; 5; 0]

C = [5; 0; 0]

D = [0; 0; 0]

define a cube

A B C D E F G H

. Find the distance between the line

A B

and the plane

E F G

5

3

4

6

9000101110

Level:

The points

A = [0; 5; 0]

B = [5; 5; 0]

C = [5; 0; 0]

D = [0; 0; 0]

define a cube

A B C D E F G H

. Find the distance between the point

A

and the point

F

\sqrt{50}

\sqrt{5}

5

10

9000101901

Level:

Find the angle between two lines and round your answer to the nearest minute.

\begin{aligned} p : x & = 2 - t, \\ y & = 3 t, \\ z & = 1; t \in R \end{aligned} \begin{aligned} q : x & = 2 s, \\ y & = 4 s, \\ z & = 1 - s; s \in R \end{aligned}

46^{\circ} 22^{'}

0^{\circ}

67^{\circ} 18^{'}

90^{\circ}

9000101902

Level:

Given points

A = [0; 1; 2]

B = [1; 2; 0]

C = [1; 2; 3]

, find the angle between the lines

A B

and

A C

. Round your answer to the nearest degree.

90^{\circ}

0^{\circ}

30^{\circ}

60^{\circ}

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