# Vector fields

## Main Question or Discussion Point

Hey - I'm stuck on a concept:

Are ALL vector fields expressable as the product of a scalar field $$\varphi$$ and a constant vector $$\vec{c}$$?

i.e. Is there always a $$\varphi$$ such that

$$\vec{A}$$ = $$\varphi$$ $$\vec{c}$$ ?

for ANY field $$\vec{A}$$?

I ask because there are some derivations from Stokes' theorem that follow from this idea, and I'm not sure these rules apply to all vector fields, because surely there are some vector fields that can't be expressed as such a product.

mathman
What is the definition of vector field that you are using?

I'm not sure exactly what you mean, but my understanding of a vector field in this context is that it's a field in a coordinate system where each component is a function of the coordinates of that point, e.g.
$$\vec{A}(x,y,z) = (x^2 - y^2, xz, y^3 + xz^2)$$

Last edited:
mathman