JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 30

The line of shortest distance between the lines $\dfrac{x-2}0=\dfrac{y-1}1=\dfrac z1$ and $\dfrac{x-3}2=\dfrac{y-5}2=\dfrac{z-1}1$ makes an angle of $\cos^{-1}\left(\sqrt{\dfrac2{27}}\right)$ with the plane $P:ax-y-z=0$, $(a>0)$. If the image of the point $(1,1,-5)$ in the plane P is $(\alpha,\beta,\gamma)$, then $\alpha+\beta-\gamma$ is equal to ______.