Coordinate Geometry: JEE Main 2020 Mathematics question

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