We use inverted finite element method (IFEM) for computing three-dimensional vector potentials and for solving div-curl systems in the whole space . IFEM is substantially different from the existing approaches since it is a non truncature method which preserves the unboundness of the domain. After developping the method, we analyze its convergence in term of weighted norms. We then give some three-dimensional numerical results which demonstrate the efficiency and the accuracy of the method and confirm its convergence.