JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 23

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 $\dfrac{x+1}{a^2+b^2}=\dfrac{y-2}{a^2-b^2}=\dfrac z1$ and the plane $x-y+z=0$ is (α, β, γ), then α + β + γ is equal to _______.