A **vector function** is any function whose output is a vector.

Parametric equations are often represented as vector functions in the following manner. This example has a single input () and produces three simultaneous outputs all which are functions of in themselves. The sum of the three components produces the radius vector.

Another example would be a vector function with coordinates as inputs, in the form

This equation represents a two-dimensional vector field.

The derivative of a vector function is equal to The integral of a vector function is equal to