# Definition:Cartesian 3-Space/Coordinate Planes

< Definition:Cartesian 3-Space(Redirected from Definition:Coordinate Planes of Cartesian 3-Space)

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## Definition

Consider the **Cartesian $3$-space** defined by $3$ distinct perpendicular planes through the origin $O$.

These $3$ planes are known as the **coordinate planes** of the Cartesian $3$-space.

### $x$-$y$ Plane

The **$x$-$y$ plane** is the Cartesian plane embedded in Cartesian $3$-space which contains the $x$-axis and the $y$-axis.

It consists of all the points in $S$ such that $z = 0$.

### $y$-$z$ Plane

The **$y$-$z$ plane** is the Cartesian plane embedded in Cartesian $3$-space which contains the $y$-axis and the $z$-axis.

It consists of all the points in $S$ such that $x = 0$.

### $x$-$z$ Plane

The **$x$-$z$ plane** is the Cartesian plane embedded in Cartesian $3$-space which contains the $x$-axis and the $z$-axis.

It consists of all the points in $S$ such that $x = 0$.

## Sources

- 1934: D.M.Y. Sommerville:
*Analytical Geometry of Three Dimensions*... (previous) ... (next): Chapter $\text I$: Cartesian Coordinate-system: $1.1$. Cartesian coordinates - 1967: D.E. Bourne and P.C. Kendall:
*Vector Analysis*... (previous) ... (next): Chapter $1$: Rectangular Cartesian Coordinates and Rotation of Axes: $1.1$ Rectangular cartesian coordinates