Why Does Vector Potential Align with Current in Infinite Distributions?

[Kolahal Bhattacharya]

We know in all ordinary cases the direction of vector potential will be mimic to the direction of current.As it is evident from the expression of A=(mu/4*pi) int{J /(r-r')}dV which is valid only for finite current distributions.
But in example 5.12 and in exercise 5.25 Griffiths has given situations where current distributions extend upto infinity.But,still the direction of A is the same as direction of J .Can you help me to reconcile these two apparently contrasting views?

 

[Ahmes]

We know in all ordinary cases the direction of vector potential will be mimic to the direction of current.

You do know it is gauge dependent, right (The formula you brought works for Coulomb)? I don't know about the example you talked about.