The perpendicular bisector of the line segment  with end points2,3,2 and −4,1,4 passes through the point  −3,6,1and has equation of the form x+3a=y−6b=z−1cwhere a,b,c are relatively prime integers with a>0 , then the value of abc−a+b+c is

The midpoint of the line segment joining 2,3,2,−4,1,4is2−42,3+12,2+42=−1,2,3  Given that the perpendicular bisector is passing through the point −3,6,1 alsoHence the equation of the perpendicular bisector is  x+3−1+3=y−62−6=z−13−1Rewrite the above equation as  x+3−1+3=y−62−6=z−13−1Comparing this with the given linea=1,b=−2,c=1Consider the expression abc−a+b+c=−2−0=−2