He has no house which to live in中不定式的to live in可以直接做house的定语,不定式的宾语就是house,再让which当宾语是多余的；而在He has no house in which to live中,which抢先做了介词in的宾语,那么整个的in which to live这个部分没有多余的宾语,故可以用来做house的定语.