Through any space point **O** we draw three mutually perpendicular straight lines. Their accepted names are: axis **Ox** **(axis of the abscissas)**, axis **Oy** **(axis of the ordinates)**, axis **Oz**. Point **O** is called the **origin of the coordinates**. On these straight lines one gives unit vectors **i** (in the direction of axis **Ox**), **j** (in the direction of axis **Oy**), **k** (in the direction of axis **Oz**).

Let **M** be a space point. The point gives a vector **OM**; **M**_{1}, **M**_{2}, **M**_{3} are correspondingly the orthogonal projections of the point **M** on the axes **Ox**, **Oy**, **Oz**. Then

**OM** = **OM**_{1} + OM_{2} + OM_{3} = x**i** + y**j** + z**k**

The numbers **x, y, z** are called the coordinates of the point **M** or the vector **OM**. This coordinate system is called the **Cartesian coordinate system** or the **rectangular coordinate system**. Each the three numbers **(x;y;z)** give the only point M.

It follows that a Cartesian coordinate system states one-to-one correspondence between a space point set and an ordered three real number set.