Which of the following represents the symmetric equations of a line in three-dimensional space?

$$\frac{x-x_o}{a}=\frac{y-y_o}{b}=\frac{z-z_o}{c}$$

$$\overrightarrow{r}=\overrightarrow{r_o}\ +t\overrightarrow{v}$$

$$x=x_o\ +\ at,\ \ y=y_o\ +\ bt,\ \ z=z_o\ +\ ct,\ $$

Which of the following represents the vector equation of a line in three-dimensional space?

$$\overrightarrow{r}=\overrightarrow{r_o}\ +t\overrightarrow{v}$$

$$x=x_o\ +\ at,\ \ y=y_o\ +\ bt,\ \ z=z_o\ +\ ct,\ $$

$$\frac{x-x_o}{a}=\frac{y-y_o}{b}=\frac{z-z_o}{c}$$

Find the parametric equations of the line through (-2, 1, 5) and parallel to the vector <4, -1, -7>.

x = -2 + 4t, y = 1 - t, z = 5 - 7t

x = -4 + 2t, y = 1 - t, z = 7 - 5t

x = -4 - 2t, y = 1 + t, z = 7 + 5t

x = -2 - 4t, y = 1 + t, z = 5 + 7t

Which of the following represents the linear equation of a plane?

$$\overrightarrow{n}\cdot\left(\overrightarrow{r}-\overrightarrow{r_o}\right)=0$$

$$a\ \left(x-x_o\right)+b\ \left(y-y_o\right)+c\left(z-z_o\right)=0$$

Which of the following represents the scalar equation of a plane?

$$a\ \left(x-x_o\right)+b\ \left(y-y_o\right)+c\left(z-z_o\right)=0$$

$$\overrightarrow{n}\cdot\left(\overrightarrow{r}-\overrightarrow{r_o}\right)=0$$

Which of the following represents the vector equation of a plane?

$$\overrightarrow{n}\cdot\left(\overrightarrow{r}-\overrightarrow{r_o}\right)=0$$

$$a\ \left(x-x_o\right)+b\ \left(y-y_o\right)+c\left(z-z_o\right)=0$$

Equations of Lines and Planes

Quiz

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.B.5

Standards-aligned

Anthony Clark

FREE Resource

20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the equations below does NOT represent the line through the points A(-1,2,3) and B(2,-1,4)?

2.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The Cartesian equation of the plane through A(-2,1,4) with vector n =3i-j+2k normal to the plane is:

-2x + y + 4z + 1 = 0

3x - y + 2z + 1 = 0

-2x + y + 4z - 1 = 0

3x - y + 2z - 1 = 0

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

3x + y + 8z - 29 = 0

3x + y + 8z + 29 = 0

x + 2y + 3z - 29 = 0

-2x + y -5z + 29 = 0

4.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The equation of the plane containing the line and the point (1,-1, 0 )

5.

DRAG AND DROP QUESTION

1 min • 1 pt

If we know the slope (m) of a line, we can write the equation for a parallel line with a point (x1, y1) using the line formula (a) = (b) * (c) .

(y - y1)

m

(x - x1)

6.

MATH RESPONSE QUESTION

1 min • 1 pt

Find the slope of a line parallel to 6x - 2y = 8

Mathematical Equivalence

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Equations of Lines and Planes

20 questions

Which of the equations below does NOT represent the line through the points A(-1,2,3) and B(2,-1,4)?

The Cartesian equation of the plane through A(-2,1,4) with vector n =3i-j+2k normal to the plane is:

The equation of the plane containing the line and the point (1,-1, 0 )

If we know the slope (m) of a line, we can write the equation for a parallel line with a point (x1, y1) using the line formula (a) = (b) * (c) .

Find the slope of a line parallel to 6x - 2y = 8

Which equation represents the line that passes through the
points (- 7, 4) and (- 6, - 2)?

(a)

The acute angle between the planes 3y - z = 4 and
x + y - 2z = 465
is

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Equations of Lines and Planes

20 questions

Which of the equations below does NOT represent the line through the points A(-1,2,3) and B(2,-1,4)?

The Cartesian equation of the plane through A(-2,1,4) with vector n =3i-j+2k normal to the plane is:

The equation of the plane containing the line and the point (1,-1, 0 )

If we know the slope (m) of a line, we can write the equation for a parallel line with a point (x1, y1) using the line formula​ ​ (a) = ​ (b) * ​ (c) .

Find the slope of a line parallel to 6x - 2y = 8

Which equation represents the line that passes through thepoints (- 7, 4) and (- 6, - 2)? (a)

The acute angle between the planes 3y - z = 4 and x + y - 2z = 465is

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

If we know the slope (m) of a line, we can write the equation for a parallel line with a point (x1, y1) using the line formula (a) = (b) * (c) .

Which equation represents the line that passes through the
points (- 7, 4) and (- 6, - 2)?

(a)

The acute angle between the planes 3y - z = 4 and
x + y - 2z = 465
is