Let $\mathrm{A}(1,0), \mathrm{B}(6,2)$ and $\mathrm{C}\left(\frac{3}{2}, 6\right)$ be the vertices of a triangle $A B C$. If $P$ is a point inside the triangle ABC such that the triangles $\mathrm{APC}, \mathrm{APB}$ and BPC have equal areas, then the length of the line segment PQ , where Q is the point $\left(-\frac{7}{6},-\frac{1}{3}\right)$, is. $\_\_\_\_$ .