1. The problem statement, all variables and given/known data I was reading a note from the class and don't understand something. Let a,b be everywhere linearly independent 1-forms on 5 dimensional manifold. Let N be 3dimensional submanifold of M. Let c,d,e be 1-forms on M such that linearly independent when restricted on N. We assume a,b,c,d,e forms a basis. Then a 1-form j will vanish on N iff j ^ a^ b does not vanish on N. 2. Relevant equations I don't understand why 1-form j will vanish on N iff j ^ a^ b does not vanish on N. 3. The attempt at a solution Suppose j vanishes on N, then j=ra+sb for some real r,s.(since c,d,e forms a basis of 1-forms on N?) But j^a^b=ra^a^b+sb^a^b=0.