Let the image of the point P (1,6, a) in the line L: x/1=(y-1)/2=(z-a+1)/b, b>0, be (a/3, 0, a+c). If S (α, β, γ), α>0, is the point on L such that…

Let the image of the point $\displaystyle \mathrm{P}(1,6, a)$ in the line $\displaystyle \mathrm{L}: \frac{x}{1}=\frac{y-1}{2}=\frac{z-a+1}{b}, b>0$, be $\displaystyle \left(\frac{a}{3}, 0, a+c\right)$. If $\displaystyle \mathrm{S}(\alpha, \beta, \gamma), \alpha>0$, is the point on L such that the distance of S from the foot of perpendicular from the point P on L is $\displaystyle 2 \sqrt{14}$, then $\displaystyle \alpha+\beta+\gamma$ is equal to: