Plane Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
What is the equation of the xy-plane in 3D space?

Solution

  1. 1
    Step 1: The xy-plane contains all points where the z-coordinate is zero.
  2. 2
    Step 2: In the general plane equation ax+by+cz=dax + by + cz = d, we want z = 0 for all points on this plane.
  3. 3
    Step 3: Set a=0,b=0,c=1,d=0a=0, b=0, c=1, d=0: the equation is z=0z = 0.

Answer

z=0z = 0
The xy-plane is defined by all points (x,y,0)(x, y, 0) โ€” it is the familiar 2D coordinate plane embedded in 3D space. Its normal vector is (0,0,1)(0,0,1), pointing straight up.

About Plane

A perfectly flat surface extending infinitely in all directions with zero thickness; defined by three non-collinear points.

Learn more about Plane โ†’

More Plane Examples