If the lines $$\frac{{x + 2}}{{4\lambda + 1}} = \frac{{y - 1}}{4} = \frac{z}{{ - 18}}$$      and $$\frac{x}{{ - 3}} = \frac{{y + 1}}{{5\mu - 3}} = \frac{{z - 1}}{6}$$      are parallel to each other then the value of the pair $$\left( {\lambda ,\,\mu } \right)$$  is :

Solution :
Direction ratios of the lines are $$4\lambda + 1,\,4,\, - 18,$$     and $$ - 3,\,5\mu - 3,\,6.$$
They are parallel
$$\eqalign{ & \Rightarrow \frac{{4\lambda + 1}}{{ - 3}} = \frac{4}{{5\mu - 3}} = \frac{{ - 18}}{6} \cr & \Rightarrow \frac{{4\lambda + 1}}{{ - 3}} = - 3{\text{ and }}\frac{4}{{5\mu - 3}} = - 3 \cr} $$