Let P_1 be the plane 3 x-y-7 z=11 and P_2 be the plane passing through the points (2,-1,0),(2,0,-1), and (5,1,1). If the foot of the perpendicular…

Let $\displaystyle \mathrm{P}_1$ be the plane $\displaystyle 3 x-y-7 z=11$ and $\displaystyle \mathrm{P}_2$ be the plane passing through the points $\displaystyle (2,-1,0),(2,0,-1)$, and $\displaystyle (5,1,1)$. If the foot of the perpendicular drawn from the point $\displaystyle (7,4,-1)$ on the line of intersection of the planes $\displaystyle \mathrm{P}_1$ and $\displaystyle \mathrm{P}_2$ is $\displaystyle (\alpha, \beta, \gamma)$, then $\displaystyle \alpha+\beta+\gamma$ is equal to $\displaystyle \_\_\_\_$.