Perpendicular Lines and Plane Intersection

Let a line with direction ratios a,−4a,−7 be perpendicular to the lines with direction ratios 3,−1,2b and b,a,−2. If the point of intersection of the line ‌

x+1

a2+b2

=‌

y−2

a2−b2

=‌

z

1

and the plane x−y+z=0 is (α,β,γ), then α+β+γ is equal to _______.