Let $E\rightarrow D$ be a complex rank two vector bundle over a compact complex 
one dimensional manifold $D$. Let $L_1, L_2 \subset E$ be rank one subbundles of E 
(i.e. line bundles). Let 
$$ n_1:= <c_1(L_1), ~~[D]>, ~~n_2 := <c_1(L_2), ~~[D]>, ~~n_3:= <c_1(E), ~~[D]>. $$
If I know the values of $n_1, n_2$ and $n_3$, is this sufficient information 
to calculate the topological intersection number $N$
$$ N:= \mathbb{P}L_1 \cdot \mathbb{P}L_2 $$
inside $\mathbb{P}E$, where $\mathbb{P}$ denotes projectivization of a bundle. 
In particular is there a formula for $N$ in terms of $n_1$, $n_2$ and $n_3$?
If not, what further information is required to calculate $N$?