Space geometry

1003124001

Level:

We are given a straight line

q = {[3 t; 2 - 2 t; 1 + t], t \in R}

and four points

A = [- 6; 6; - 1]

B = [- 3; 0; 0]

C = [0; 2; 1]

and

D = [3; 0; 2]

. Out of the given points select all that lie on the straight line

q

. (Choose the corresponding option.)

A

C

D

B

C

D

B

C

A

B

C

1003124002

Level:

From the given options choose the parametric equations which describe a straight line

p

passing through the points

A = [- 2; 0; 1]

and

B = [2; 0; - 3]

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

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

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

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

1003124003

Level:

Find the missing coordinates of the point

B = [x_{B}; y_{B}; - 3]

lying on a straight line

p

defined by the parametric equations

\begin{aligned} p : x & = - 1 + \frac{1}{4} m, \\ y & = 2 + m, \\ z & = 5 - m; m \in R . \end{aligned}

B = [1; 10; - 3]

B = [- 3; - 6; - 3]

B = [1; 3; - 3]

B = [- 3; 6; - 3]

1003124004

Level:

Find the value of a parameter

a \in R

so that the point

B = [1; 4; 5]

lies on the straight line

p

defined by the parametric equations

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

a = 1

a = - 1

a = 2

no such value of

a

exists

1003124005

Level:

Find the value of a parameter

a \in R

so that the point

C = [2; 0; 6]

lies on the straight line

p

defined by the parametric equations

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

a = - 3

a = 0

a = - 1

no such values of

a

exists

1003124006

Level:

Find the value of a parameter

a \in R

so that the point

D = [- 2; 1; 1]

lies on the straight line

p

defined by the parametric equations

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

no such values of

a

exists

a = - 1

a = 0

a = 1

1003164401

Level:

Let a straight line

p

be defined by parametric equations:

\begin{aligned} x & = - 1 + 2 t, \\ y & = 2 + t, \\ z & = 5 - t; t \in R . \end{aligned}

Find the coordinates of the intersection point

M

of the line

p

with the

x y

-coordinate plane.

M = [9; 7; 0]

M = [0; 0; 5]

M = [- 1; 2; 0]

M = [0; 0; - 1]

1003164402

Level:

Let a straight line

p

be defined by parametric equations:

\begin{aligned} x & = - 1 + 2 t, \\ y & = 2 + t, \\ z & = 5 - t; t \in R . \end{aligned}

Find the coordinates of the intersection point

M

of the line

p

with the

x z

-coordinate plane.

M = [- 5; 0; 7]

M = [0; 2; 0]

M = [- 1; 0; 5]

M = [2; 0; - 1]

1003164403

Level:

Let a straight line

p

be defined by parametric equations:

\begin{aligned} x & = - 1 + t, \\ y & = 2 + 3 t, \\ z & = 5 - t; t \in R . \end{aligned}

Find the coordinates of the intersection point

M

of the line

p

with the

y z

-coordinate plane.

M = [0; 5; 4]

M = [- 1; 0; 0]

M = [0; 3; - 1]

M = [1; 0; 0]

1003164404

Level:

Let a straight line

p

be defined by parametric equations:

\begin{aligned} x & = 3 + t, \\ y & = 2 - t, \\ z & = 4; t \in R . \end{aligned}

Find the coordinates of the intersection point

M

of the line

p

with the

x y

-coordinate plane.

There is no such point

M

M = [0; 0; 4]

M = [- 3; 2; 0]

M = [1; - 1; 0]

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