Let L be the line of intersection of planes r ·( i - j +2 k )=2 and r ·(2 i + j - k )=2. If P (α, β, γ) is the foot of perpendicular on L from the…

Let L be the line of intersection of planes $\displaystyle \overrightarrow{\mathrm{r}} \cdot(\hat{i}-\hat{j}+2 \hat{k})=2$ and $\displaystyle \overrightarrow{\mathrm{r}} \cdot(2 \hat{i}+\hat{j}-\hat{k})=2$. If $\displaystyle \mathrm{P}(\alpha, \beta, \gamma)$ is the foot of perpendicular on L from the point ($\displaystyle 1$, $\displaystyle 2$, $\displaystyle 0$), then the value of $\displaystyle 35(\alpha+\beta+\gamma)$ is equal to :