Space geometry

9000101903

Level:

Given points

A = [- 1; 0; 3]

B = [0; 2; 0]

, find the angle between the line

A B

and the line

m

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

Round your answer to the nearest minute.

72^{\circ} 45^{'}

0^{\circ}

48^{\circ} 15^{'}

90^{\circ}

9000101904

Level:

Find the angle between the

x

-axis and the line

p

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

Round your answer to the nearest minute.

71^{\circ} 34^{'}

0^{\circ}

69^{\circ} 17^{'}

90^{\circ}

9000101905

Level:

The points

A = [0; 5; 0]

B = [5; 5; 0]

C = [5; 0; 0]

D = [0; 0; 0]

define the cube

A B C D E F G H

. Find the angle between the lines

B F

and

A C

. Round your answer to the nearest minute.

90^{\circ}

0^{\circ}

45^{\circ}

73^{\circ} 47^{'}

9000101906

Level:

Find the angle between the planes

α

and

β

α : 2 x - 5 y + 3 z - 4 = 0, β : x - 3 = 0

Round your answer to the nearest minute.

71^{\circ} 4^{'}

21^{\circ} 42^{'}

82^{\circ} 19^{'}

85^{\circ} 2^{'}

9000101907

Level:

The general plane

α

has the equation

α : 3 z - 4 = 0

and the plane

β

has a normal vector

\vec{n} = (0; 0; 1)

. Find the angle between

α

and

β

and round your answer to the nearest degree.

0^{\circ}

30^{\circ}

45^{\circ}

90^{\circ}

9000101908

Level:

Find the angle between the line

p

and the plane

α

α : x - 3 z + 5 = 0; \begin{aligned} p : x & = 3, \\ y & = 3 t, \\ z & = 1 - t; t \in R \end{aligned}

Round your answer to the nearest minute.

17^{\circ} 27^{'}

0^{\circ}

47^{\circ} 33^{'}

90^{\circ}

9000101909

Level:

Given points

A = [1; 0; 2]

B = [1; 0; 0]

and the plane

α

α : 2 x - 4 y = 0,

find the angle between the line

A B

and the plane

α

. Round your answer to the nearest minute.

0^{\circ}

22^{\circ} 48^{'}

45^{\circ} 19^{'}

90^{\circ}

9000101910

Level:

The points

A = [0; 5; 0]

B = [5; 5; 0]

C = [5; 0; 0]

and

D = [0; 0; 0]

define the cube

A B C D E F G H

. Find the angle between the line

B F

and the plane

A F E

. Round your answer to the nearest minute.

0^{\circ}

35^{\circ} 16^{'}

45^{\circ}

90^{\circ}

9000106301

Level:

Find the line

k

which is perpendicular to the plane

α

α : 2 x + y - z - 5 = 0

and passes through the point

A = [0; 0; 1]

\begin{aligned} x & = 2 t, \\ y & = t, \\ z & = 1 - t; t \in R \end{aligned}

\begin{aligned} x & = 2 + 2 m, \\ y & = 1 + m, \\ z & = - 1 - m; m \in R \end{aligned}

\begin{aligned} x & = 2 k, \\ y & = k, \\ z & = - k; k \in R \end{aligned}

\begin{aligned} x & = 2, \\ y & = 1, \\ z & = - 1 + u; u \in R \end{aligned}

9000106302

Level:

The plane

α

has equation

α : 2 x + y - z - 5 = 0.

The line

k

passes through the point

A = [0; 0; 1]

and is perpendicular to

α

. Find the intersection

S

of the line

k

and the plane

α

S = [2; 1; 0]

S = [2; 0; 1]

S = [- 2; 1; 0]

S = [- 2; 0; 1]

9000101903

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