Let a, b, c the direction ratios of the line passing through the point (1, - 2, 3).
∴    equations of line are
                                                         ...(1)
Since line (1) parallel to the plane x - y + 2z = 5 whose direction ratios of the normal are 1, -1, 2
∴  a(1) +b(– 1) + c(2) = 0
or    a – b +2c=0    ... (2)
Again line (1) is parallel to the plane 3x + 2y – z = 6
∴ 3a + 2b – c = 0    ...(3)
From (2) and (3), we get
                   

∴ from (1), the equations of line are