Prove that the definition of incidence is independent of the choice of the representatives of p and

Question:

Prove that the definition of incidence is independent of the choice of the representatives of p and L. That is, if p1, p2, p3, and q1, q2, q3 are two triples of homogeneous coordinates for p, and L1, L2, L3, and M1, M2, M3 are two triples of homogeneous coordinates for L, prove that p1L1 + p2L2 + p3L3 = 0 if and only if q1M1 + q2M2 + q3M3 = 0.