Equipollent Vector

Two vectors AB and CD are considered equipollent if they share the same magnitude, direction, and orientation.

Equipollence is a relation of equivalence.

Equipollence vectors can also originate from different points. It is not required for them to share the same starting point.

Properties of Equivalent Vectors

The properties of equivalent vectors include:

• Reflexive Property. Every vector is equivalent to itself.
• Symmetric Property. If vector AB is equivalent to CD, then vector CD is also equivalent to AB.
• Transitive Property. If vector AB is equivalent to CD and vector CD is equivalent to EF, then vector AB is equivalent to EF.

The Equivalence Class

Equivalent vectors in a plane form a set known as an equivalence class.

Each equivalence class is simply referred to as a vector.

This is a set containing all the vectors in the plane that have the same magnitude, direction, and orientation.