Definition:Cartesian 3-Space/Orientation

Definition


Consider a Cartesian $3$-Space.

Let the $x$-axis, $y$-axis and $z$-axis be defined.

Let a point $P$ be identified on the $x$-axis, different from $O$, with the coordinate pair $\tuple {1, 0}$ in the $x$-$y$ plane.

Let the point $P'$ be identified on the $y$-axis such that $OP' = OP$.

It remains to identify the point $P$ on the $z$-axis such that $OP = OP$.