If the distances of the point (1,2, a) from the line (x-1)/1=y/2=(z-1)/1 along the lines L_1: (x-1)/3=(y-2)/4=(z-a)/b and L_2:…

If the distances of the point $\displaystyle (1,2, a)$ from the line $\displaystyle \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$ along the lines $\displaystyle \mathrm{L}_1: \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$ and $\displaystyle \mathrm{L}_2: \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$ are equal, then $\displaystyle a+b+c$ is equal to