Are

**ALL**vector fields expressable as the product of a scalar field [tex]\varphi[/tex] and a constant vector [tex]\vec{c}[/tex]?

i.e. Is there always a [tex]\varphi[/tex] such that

[tex]\vec{A}[/tex] = [tex]\varphi[/tex] [tex]\vec{c}[/tex] ?

for ANY field [tex]\vec{A}[/tex]?

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.