Matrices And Determinants

Let for any three distinct consecutive terms \(a, b, c\) of an A.P, the lines \(a x+b y+c=0\) be concurrent at the point \(P\) and \(Q(\alpha, \beta)\) be a point such that the system of equations

$$\begin{aligned} & x+y+z=6, \\ & 2 x+5 y+\alpha z=\beta \text { and } \end{aligned}$$

\(x+2 y+3 z=4\), has infinitely many solutions. Then \((P Q)^2\) is equal to _________.