Let Ox, Oy, and Oz be three mutually perpendicular directed lines, intersecting at the point O. In the order Ox, Oy, Oz, they form a right-handed system if a person standing erect in the positive z-direction and facing the positive y-direction would have the positive x-direction to their right. Typically, right-handed systems are used in calculations and diagrams.

The three directed lines Ox, Oy, and Oz (in that order) form a right-handed system, but if taken in the order Oy, Ox, Oz, they form a left-handed system. If the direction of any one of three lines of a right-handed system is reversed, the three directed lines form a left-handed system.

Similarly, an ordered set of three oblique directed lines may be described as forming a right- or left-handed system. Three vectors, in a given order, form a right- or left-handed system if directed line segments representing them define directed lines that do so. For independent vectors u and v the vector product is defined so that u,v and u × v form a right-handed system.