8.5 The Cartesian Equation of a Plane
Chapter
Chapter 8
Section
8.5
Purchase this Material for $10
You need to sign up or log in to purchase.
Subscribe for All Access
You need to sign up or log in to purchase.
Lectures 4 Videos
  1. Proof of Scalar Equation of Plane5 months
Buy to View
8.08mins
Proof of Scalar Equation of Plane
  1. Converting a Vector Form of a Plane to Scalar Form example
Buy to View
3.36mins
Converting a Vector Form of a Plane to Scalar Form example
  1. Converting Scalar equation of the Plane to Vector Form
Buy to View
2.03mins
Converting Scalar equation of the Plane to Vector Form
  1. Determining relationship between two planes using the normals
Buy to View
5.37mins
Determining relationship between two planes using the normals
Solutions 20 Videos

A plane is defined by the equation x -7y - 18z = 0.

a) What is a normal vector to this plane?

b) Explain how you know that this plane passes through the origin.

c) Write the coordinates of three points on this plane.

Buy to View
1.24mins
Q1

A plane is defined by the equation 2x - 5y = 0.

a) What is a normal vector to this plane?

b) Explain how you know that this plane passes through the origin.

c) Write the coordinates of three points on this plane.

Buy to View
1.16mins
Q2

A plane is defined by the equation x= 0.

a) What is a normal vector to this plane?

b) Explain how you know that this plane passes through the origin.

c) Write the coordinates of three points on this plane.

Buy to View
1.17mins
Q3

b) A plane has a normal of \vec{n} = (-\displaystyle{\frac{1}{2}}, \displaystyle{\frac{3}{4}}, \displaystyle{\frac{7}{16}}) and passes through the origin. Determine the Cartesian equation of this plane.

Buy to View
0.27mins
Q4b

A plane is determined by a normal, \vec{n} = (1, 7, 5), and contains the point P(-3, 3, 5). Determine a Cartesian equation.

Buy to View
0.00mins
Q5

Determine the Cartesian equation of the plane that contains the points A(-2, 3, 1), B(3, 4, 5), and C(1, 1, 0).

Buy to View
1.53mins
Q7

The line with vector equation \vec{r} = (2, 0, 1) + t(-4, 5, 5), s\in \mathbb{R}, lies on the plane \pi, as does the point P(1, 3, 0). Determine the Cartesian equation of \pi.

Buy to View
2.08mins
Q8

Determine unit vectors that are normal to each of the following planes:

3x - 4y + 12z - 1 = 0

Buy to View
0.56mins
Q9c

A plane contains the point A(2, ,2 -1) and the line \vec{r} = (1, 1, 5) + s(2, 1, 3), s \in \mathb{R}. Determine the Cartesian equation of this plane.

Buy to View
2.05mins
Q10

Determine the Cartesian equation of the plane containing the point (-1, 1, 0) and perpendicular to the line joining points (1, 2, 1) and (3, -2, 0).

Buy to View
2.01mins
Q11

a. Explain the process you would use to determine the angle formed between two intersecting planes.

b. Determine the angle between the planes x + 2y - 3z - 4 =0 and x + 2y - 1=0.

Buy to View
2.43mins
Q12

a) Determine the angle between the planes x + 2y - 3z - 4 = 0 and x + 2y - 1 = 0.

Buy to View
3.15mins
Q13a

Determine the Cartesian equation of the plane that passes through the point P(1, 2, 1) and is perpendicular to the line \displaystyle{\frac{x - 3}{-2}} = \displaystyle{\frac{y + 1}{3}} = \displaystyle{\frac{z +4}{1}}.

Buy to View
1.49mins
Q13b

What is the value of k that makes the planes 4x + ky - 2z + 1 = 0 and 2x + 4y - z + 4 = 0 parallel .

Buy to View
0.43mins
Q14a

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

What is the value of k that makes these two planes perpendicular?

Buy to View
0.32mins
Q14b

Can these two planes: 4x + ky - 2z + 1 = 0 and 2x + 4y - z + 4 = 0

ever be coincident? Explain.

Buy to View
0.35mins
Q14c

Determine the Cartesian equation of the plane that passes through the points (1, 4, 5) and (3, 2, 1) and it s perpendicular to the plane 2x - y + z - 1 = 0.

Buy to View
3.12mins
Q15

Determine an equation of the plane that is perpendicular to the plane x + 2y + 4= 0, contains the origin, and has a normal that makes an angle of 30^{\circ} with the z-axis.

Buy to View
3.07mins
Q16

Determine the equation of the plane that lies between the points (-1, 2, 4) and (3, 1, -4) and is equidistant from them.

Buy to View
2.59mins
Q17