If the length of the perpendicular drawn from the point P ( a, 4,2), a >0 on the line (x+1)/2=(y-3)/3=(z-1)/-1 is 2 √ 6 units and Q (α_1, α_2, α_3)…

If the length of the perpendicular drawn from the point $\displaystyle \mathrm{P}(\mathrm{a}, 4,2), \mathrm{a}>0$ on the line $\displaystyle \frac{x+1}{2}=\frac{y-3}{3}=\frac{z-1}{-1}$ is $\displaystyle 2 \sqrt{6}$ units and $\displaystyle \mathrm{Q}\left(\alpha_1, \alpha_2, \alpha_3\right)$ is the image of the point P in this line, then $\displaystyle \mathrm{a}+\sum_{i=1}^3 \alpha_i$ is equal to :