Subsheaves of a locally free sheaf on $P^{d}$

Question

Suppose $G$ is a locally free sheaf on $P^{d}$. $F_{1}$,$F_{2}$ are two subsheaves of
$G$ and they concide on a dense open subscheme of $P^{d}$ .If the quotients of $G$ corresponding to these two subsheaves are torsion free,can we conclude that $F_{1}=F_{2}$ everywhere?

Answer 1

Let $F_3 = F_1 + F_2$. Then $F_3$ coincides with $F_1$ and $F_2$ on the same dense open. Therefore $F_3/F_1$ and $F_3/F_2$ are torsion. But they are also torsion free, as subsheaves of $G/F_1$ and $G/F_2$, so they are zero, and $F_1 = F_3 = F_2$.