If the length of the perpendicular drawn from the point $P(a,4,2),;a>0$ on the line $\dfrac{x+1}{2}=\dfrac{y-3}{3}=\dfrac{z-1}{-1}$ is $2\sqrt{6}$ units and $Q(\alpha_{1},\alpha_{2},\alpha_{3})$ is the image of the point $P$ in this line, then $a+\sum_{i=1}^{3}\alpha_{i}$ is equal to: