Let a triangle PQR be such that P and Q lie on the line (x+3)/8=(y-4)/2=(z+1)/2 and are at a distance of 6 units from R (1, 2, 3). If (α, β, γ) is…

Let a triangle PQR be such that P and Q lie on the line $\displaystyle \frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ and are at a distance of $\displaystyle 6$ units from R ($\displaystyle 1$, $\displaystyle 2$, $\displaystyle 3$). If $\displaystyle (\alpha, \beta, \gamma)$ is the centroid of $\displaystyle \Delta \mathrm{PQR}$, then $\displaystyle \alpha+\beta+\gamma$ is equal to: