MathNet 2012 Question 71

Let $P$ be a point on the image of $y = x + \frac{2}{x}$ ($x \gt 0$). Through $P$ draw lines perpendicular to $y = x$ and $y$-axis with foot points $A, B$, respectively. Then the value of $\vec{PA} \cdot \vec{PB}$ is ______.