It is a hot issue to allocate resources using auction mechanisms in vehicular fog computing (VFC) with cloud and edge collaboration. However, most current research faces the limitation of only considering single type resource allocation, which cannot satisfy the resource requirements of users. In addition, the resource requirements of users are satisfied with a fixed amount of resources during the usage time, which may result in high cost of users and even cause a waste of resources. In fact, the actual resource requirements of users may change with time. Besides, existing allocation algorithms in the VFC of cloud and edge collaboration cannot be directly applied to time-varying multidimensional resource allocation. Therefore, in order to minimize the cost of users, we propose a reverse auction mechanism for the time-varying multidimensional resource allocation problem (TMRAP) in VFC with cloud and edge collaboration based on VFC parking assistance and transform the resource allocation problem into an integer programming (IP) model. And we also design a heuristic resource allocation algorithm to approximate the solution of the model. We apply a dominant-resource-based strategy for resource allocation to improve resource utilization and obtain the lowest cost of users for resource pricing. Furthermore, we prove that the algorithm satisfies individual rationality and truthfulness, and can minimize the cost of users and improve resource utilization through comparison with other similar methods. Above all, we combine VFC smart parking assistance with reverse auction mechanisms to encourage resource providers to offer resources, so that more vehicle users can obtain services at lower prices and relieve traffic pressure.