Straight Lines And Pair Of Straight Lines

If the orthocentre of the triangle formed by the lines \(2 x+3 y-1=0, x+2 y-1=0\) and \(a x+b y-1=0\), is the centroid of another triangle, whose circumcentre and orthocentre respectively are \((3,4)\) and \((-6,-8)\), then the value of \(|a-b|\) is _________.