Question 82
In a plane rectangular coordinate system $xOy$, the focus of parabola $\Gamma: y^2 = 2px$ ($p \gt 0$) is $F$. Make a tangent line to $\Gamma$ passing through point $P$ (different from $O$) on $\Gamma$ and it intersects the $y$-axis at point $Q$. If $|FP| = 2$, $|FQ| = 1$, then the dot product of vectors $\overrightarrow{OP}$ and $\overrightarrow{OQ}$ is ______.