PlanetPhysics/Vector Functions

A vector function of position in space is a function

which associates with each point in space a definite vector. The function may be broken up into its three components

Examples of vector functions are very numerous in physics. Already the function has occurred. At each point of space has in general a definite vector value. In mechanics of rigid bodies the velocity of each point of the body is a vector function of the position of the point. Fluxes of heat, electricity, magnetic force, fluids, etc., are all vector functions of position in space.

The scalar operator may be applied to a vector function to yield another vector function.

Let

and

Then

and

more to come..

This is from the public domain text by Gibbs.