A line ' l ' passing through origin is perpendicular to the lines l_1: r =(3+ t ) i +(-1+2 t ) j +(4+2 t ) k; l_2: r =(3+2 s ) i +(3+2 s ) j +(2+ s )…

A line ' $\displaystyle l$ ' passing through origin is perpendicular to the lines $$\begin{aligned} & l_1: \overrightarrow{\mathrm{r}}=(3+\mathrm{t}) \hat{i}+(-1+2 \mathrm{t}) \hat{j}+(4+2 \mathrm{t}) \hat{k} \\ & l_2: \overrightarrow{\mathrm{r}}=(3+2 \mathrm{~s}) \hat{i}+(3+2 \mathrm{~s}) \hat{j}+(2+\mathrm{s}) \hat{k} \end{aligned} $$ If the co-ordinates of the point in the first octant on ' $\displaystyle l_2$ ' at a distance of $\displaystyle \sqrt{17}$ from the point of intersection of ' $\displaystyle l$ ' and ' $\displaystyle l_1$ ' are (a, b, c), then $\displaystyle 18(\mathrm{a}+\mathrm{b}+\mathrm{c})$ is equal to \_\_\_\_.