Definition:Cartesian 3-Space/Coordinate Planes
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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