Question

Is a plane that is parallel to any one of these 3 coordinate planes also considered a coordinate plane, such as x=4 or z = -3?

Answer 1

Let's examine `x = 4`

In terms of a point `(x,y,z)`

`x + 0y + 0z = 4`

The normal vector to this scalar equation to of a plane is:

`hati + 0hatj+0hatk`

A vector form of this plane is:

`(x,y,z) = (4,0,0) + s(0hati+hatj+0hatk) + t(0hati+0hatj+hatk)`

The 3 parametric equations for this plane are:

`x = 4`, `y = s`, `z=t`

It is certainly a plane.

We can do the same thing with `z=-3`

Please think of it this way:

If `x=0`, is the y-z plane, `y=0` is the x-z plane, and `z = 0` is the x-y plane, then `x = k_1` is a y-z plane with an x coordinate that is `k_1`, `y= k_2` is an x-z plane with an y coordinate that is `k_2`, and `z=k_3` is an x-y plane with a z coordinate that is `k_3`.