Help with Understanding Plane Z: x - y

  • Thread starter lecammm
  • Start date
  • Tags
    Plane
In summary, the conversation discusses the confusion surrounding the equation for a plane, z = x - y. The participants suggest starting from the general equation of a plane, Ax + By + Cz = D, and using specific values to solve for A, B, and C. It is noted that there is no single unique equation for a plane, as any multiple of the original equation is also valid."
  • #1
lecammm
9
0
Hey guys, I'm really really confused on how we come about the plane z = x - y. I always have been and it's proving to hurt my progress, any help will be accepted.
 

Attachments

  • eJJTzfd.png
    eJJTzfd.png
    16.3 KB · Views: 494
Physics news on Phys.org
  • #2
Well to help us understand how you got confused, please show us your best attempt at the problem.
 
  • #3
Start from the general equation of a plane, Ax+ By+ Cz= D, then let x= y= z= 0; x= z= 1, y= 0; and x= y= 1, z= 0; to get three equations to solve for A, B, and C. Of course, there is no "unique" equation for a plane. Any multiple, kAx+ kBy+ kCz= kD, is also an equation for the same plane.
 

1. What is Plane Z?

Plane Z is a mathematical concept that represents a two-dimensional coordinate system in which x and y are the two axes and the third axis, z, is perpendicular to the x-y plane.

2. How do I graph a plane in the x-y coordinate system?

To graph a plane in the x-y coordinate system, you will need at least three points on the plane. Plot these points on the x-y plane and connect them with straight lines to form a triangle. The plane will be the flat surface that extends infinitely in all directions through the points of the triangle.

3. What does the equation x - y = c represent in Plane Z?

In Plane Z, the equation x - y = c represents a line that is parallel to the z-axis. The value of c will determine the distance of the line from the origin along the z-axis.

4. How do I find the intersection of two planes in Plane Z?

To find the intersection of two planes in Plane Z, you will need to solve the system of equations formed by the two planes. This can be done by either substitution or elimination. The solution to the system will be the coordinates of the point where the two planes intersect.

5. Can you have more than one point on a plane in Plane Z?

Yes, a plane in Plane Z can have an infinite number of points. This is because the plane extends infinitely in all directions. However, if you are trying to graph a specific plane, you will need at least three points on the plane to accurately represent it in the x-y coordinate system.

Similar threads

Replies
6
Views
1K
Replies
3
Views
1K
Replies
32
Views
3K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
4
Views
1K
  • Calculus
Replies
1
Views
1K
  • Calculus
Replies
3
Views
1K
Back
Top