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 \(\displaystyle \frac{x+1}{a^2+b^2}=\frac{y-2}{a^2-b^2}=\frac{z}{1} \) and the plane \( x-y+z=0 \) is \( (\alpha,\beta,\gamma) \), then \( \alpha+\beta+\gamma \) is equal to __________.
