Cartesian coordinates in space

Until now we have worked in the Cartesian plane: two axes, two coordinates. Moving to space we add a third axis: three lines $x,y,z$ mutually perpendicular, oriented according to the right-hand rule (thumb $\to x$, index finger $\to y$, middle finger $\to z$). Every point is then identified by an ordered triple of numbers.

Definition — Cartesian coordinates in space

In the system of Cartesian coordinates in space every point $P$ is identified by an ordered triple $(x_P, y_P, z_P)$.

The three coordinates are read by projecting the point onto the three axes, exactly as two of them were read in the plane.

A point $P$ in space and its three coordinates, read by projecting onto the axes.

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Topics: Analytic geometry in space
Concepts: Cartesian coordinates · Cartesian plane
Skills: Analytic geometry