Three Dimensional Geometry

Let $P(\alpha, 4,7)$ and $Q(\beta, \beta, 8)$ be two points. If $Y Z$-plane divides the join of the points $P$ and $Q$ in the ratio $2: 3$ and $Z X$-plane divides the join of $P$ and $Q$ in the ratio $4: 5$, then length of line segment $P Q$ is