Notwithstanding other provisions of this article, any nonresident from a state that does not require the registration of a vehicle like that owned by such nonresident when such vehicle is owned and operated by a resident of Virginia in the state in which the foreign vehicle owned or operated by such nonresident is registered, shall not be required to register such vehicle in the Commonwealth. This section, however, shall not permit the operation of any truck, trailer, or semitrailer the weight, length, width, or height of which vehicle or combination of vehicles is in violation of the provisions of this title or at a speed in violation of this title; nor shall the privileges provided in this section apply to common carriers or passenger cars.