The equation of the plane which is equidistant from the lines  $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{1}=\frac{z-1}{2}$  is $Ax+By+Cz-9=0$  then the value of  $A+B+C=$

Equation of plane counting line  $\frac{x-2}{3}=\frac{y-3}{1}=\frac{z-1}{2}$ is
$(x-2)-3(y-3)+\lambda (2(y-3)-(z-1))=0$
$x+(2\lambda -3)y-\lambda z+7-5\lambda =\mathrm{0..............}\left(1\right)$
If the plane is parallel to  $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$
$\lambda =5$
The equation of the plane which contains second line parallel to first is  $x+7y-5z-18=0$
Similarly the equation of the plane which contains first line and parallel to second line is
$(x-1)+7(y-2)-5(z-3)=0$
$x+7y-5z=0$
Required plane is  $\frac{x+7y-5z-18+x+7y-5z}{2}=0$
$x+7y-5z-9=0$