Let P and Q be the points on the line (x+3)/8=(y-4)/2=(z+1)/2 which are at a distance of 6 units from the point R(1,2,3). If the centroid of the…

Let P and Q be the points on the line $\displaystyle \frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}$ which are at a distance of $\displaystyle 6$ units from the point $\displaystyle R(1,2,3)$. If the centroid of the triangle $\displaystyle P Q R$ is $\displaystyle (\alpha, \beta, \gamma)$, then $\displaystyle \alpha^2+\beta^2+\gamma^2$ is: