Definition:Cartesian 3-Space

Definition
The Cartesian $3$-space is a Cartesian coordinate system of $3$ dimensions.

Cartesian Coordinate Triple
Hence:
 * the point $P$ is identified with the coordinates $\tuple {1, 0, 0}$
 * the point $P'$ is identified with the coordinates $\tuple {0, 1, 0}$.
 * the point $P''$ is identified with the coordinates $\tuple {0, 0, 1}$.