Change format of equation of plane

In summary, the conversation discusses the format for writing the equation of a plane and how it relates to the given plane defined by x = 2 + t, y = 2 + t, and z = t. It is eventually discovered that it is not the equation of a plane, but rather a line. This realization is made after investigating a resource on planes and realizing it was a typo in the textbook.
  • #1
ChickenChakuro
32
0
Hi all, I have a plane defined like this:

x = 2 +t
y = 2+t
z = t

How do I put it in the format:
Ax + By + Cz = D?

I feel stupid! :confused:
 
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  • #2
So it is the line through (2,2,0) and parallel to the vector v = (1,1,1)
 
Last edited:
  • #3
Why is it not parallel to the vector v = (1,1,1)?
 
  • #4
You may want to investigate this: http://mathworld.wolfram.com/Plane.html" [Broken].
 
Last edited by a moderator:
  • #5
ChickenChakuro said:
Hi all, I have a plane defined like this:

x = 2 +t
y = 2+t
z = t

How do I put it in the format:
Ax + By + Cz = D?

I feel stupid! :confused:
Well, feel only a little bit stupid!:rolleyes: That's not the equation of a plane! Since x, y, z depend on a single parameter, t, it is the equation of a one-dimensional figure. Since the functions are linear, it is the equation of a line, not a plane.
 
  • #6
Ah ok, thanks for all the help!
 
  • #7
Guess what? Turns out it was a textbook orthographical error. It was supposed to be "line" not "plane." And I was stumped for so long!
 

1. What is the equation of a plane?

The equation of a plane is a mathematical representation of a flat surface in three-dimensional space. It is typically written in the form Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant.

2. How do you change the format of an equation of a plane?

The format of an equation of a plane can be changed by manipulating the coefficients and constants in the equation. This can involve rearranging terms, factoring, or simplifying the equation.

3. What is the standard form of an equation of a plane?

The standard form of an equation of a plane is Ax + By + Cz + D = 0, where A, B, and C are the coefficients of the x, y, and z variables, and D is a constant. This form is often used because it allows for easy identification of the plane's normal vector and distance from the origin.

4. Can you change the format of an equation of a plane to slope-intercept form?

No, slope-intercept form (y = mx + b) is used to represent lines, not planes. However, a plane's equation can be simplified to a form similar to slope-intercept form by solving for one of the variables and expressing the other two in terms of it.

5. Why would you need to change the format of an equation of a plane?

Changing the format of an equation of a plane can make it easier to visualize and understand the properties of the plane. It can also help with solving problems involving planes, such as finding intersections or determining distances between points and the plane.

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