Definition:Vector Field

Definition

If a vector quantity $\mathbf v$ can be associated with every point in a given space, then $\mathbf v$ is said to be a vector field.

Examples

Velocity of Fluid

In a moving fluid, the velocity $\mathbf v$ of the fluid is an example of a vector field.

That is, the velocity $\mathbf v$ at a point $P$ in the fluid is the velocity of the particle which is situated at $P$ at a given instant.