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?

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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?

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Answer 1 · 2017-12-19T00:43:27

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 $k_3$ .

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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?

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