Can a Vector Be Expanded into a Field in Physics?

[maburne2]

Hey everyone,
I was just wondering can a vector be expanded into a field? I.e. take a gravitational potential that can be described by a vector (F = -$$\nabla$$V). Can this vector then be expanded into a field given a plane with the point of attraction at the origin, for simplicity.

Thanks

 

[Bloodthunder]

Vectors by themselves are just something that has both magnitude and direction. But what you described (F = - del(V)) is a vector field, which... yeah, is a field.

 

[maburne2]

So if I take a vector and expand it throughout some arbitrary plane it makes a field?