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…

Let a line with direction ratios a, -4a, -$\displaystyle 7$ be perpendicular to the lines with direction ratios $\displaystyle 3$, - $\displaystyle 1$, 2b and b, a, -2. If the point of intersection of the line $\displaystyle \frac{x+1}{\mathrm{a}^2+\mathrm{b}^2}=\frac{y-2}{\mathrm{a}^2-\mathrm{b}^2}=\frac{z}{1}$ and the plane $\displaystyle x-y+z=0$ is $\displaystyle (\alpha, \beta, \gamma)$, then $\displaystyle \alpha+\beta+\gamma$ is equal to \_\_\_\_.