Let L be a line obtained from the intersection of two planes x+2 y+z=6 and y+2 z=4. If point P (α, β, γ) is the foot of perpendicular from (3, 2, 1)…

Let L be a line obtained from the intersection of two planes $\displaystyle x+2 y+z=6$ and $\displaystyle y+2 z=4$. If point $\displaystyle \mathrm{P}(\alpha, \beta, \gamma)$ is the foot of perpendicular from ($\displaystyle 3$, $\displaystyle 2$, $\displaystyle 1$) on L , then the value of $\displaystyle 21(\alpha+\beta+\gamma)$ equals: