3. Given $P$ is a point on the hyperbola $\Gamma: \frac{x^{2}}{463^{2}}-\frac{y^{2}}{389^{2}}=1$, a line $l$ is drawn through point $P$, intersecting the two asymptotes of the hyperbola $\Gamma$ at points $A$ and $B$. If $P$ is the midpoint of segment $A B$, and $O$ is the origin, then $S_{\triangle O A B}=$ $\qquad$ .
3. 180107 .

Let the two asymptotes of the hyperbola $\Gamma$ be $l_{1}: y=\frac{389}{463} x, l_{2}: y=-\frac{389}{463} x$;
$l$ intersects $l_{1} 、 l_{2}$ at points $A 、 B$ respectively. Let $P\left(x_{0}, y_{0}\right), A\left(x_{1}, \frac{389}{463} x_{1}\right)$, $B\left(x_{2},-\frac{389}{463} x_{2}\right)$.
Then $x_{0}=\frac{x_{1}+x_{2}}{2}, y_{0}=\frac{389}{463} \cdot \frac{x_{1}-x_{2}}{2}$. From $1=\frac{x_{0}^{2}}{463^{2}}-\frac{y_{0}^{2}}{389^{2}}=\frac{x_{1} x_{2}}{463^{2}}$, we have $S_{\triangle O A B}=\frac{1}{2}\left|x_{1}\left(-\frac{389}{463} x_{2}\right)-x_{2}\left(\frac{389}{463} x_{1}\right)\right|$ $=\frac{389}{463}\left|x_{1} x_{2}\right|=389 \times 463=180107$.