Definition:Cartesian 3-Space/Ordered Triple

Identification of Point in Space with Ordered Triple
Let $Q$ be a point in Cartesian $3$-space.

Construct $3$ straight lines through $Q$:
 * one perpendicular to the $y$-$z$ plane, intersecting the $y$-$z$ plane at the point $x$


 * one perpendicular to the $x$-$z$ plane, intersecting the $x$-$z$ plane at the point $y$


 * one perpendicular to the $x$-$y$ plane, intersecting the $x$-$y$ plane at the point $z$.

The point $Q$ is then uniquely identified by the ordered pair $\tuple {x, y, z}$.

Also known as
The ordered triple $\tuple {x, y, z}$ which determines the location of $P$ in the cartesian $3$-space can be referred to as the rectangular coordinates or (commonly) just coordinates of $P$.