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