Solution :
Condition for parallelism is $ \sin \theta = \overrightarrow{b} . \overrightarrow{n}=0$
The line joining the point $P(3,2,6)$ and Q which lies on the line is
$PQ= (-3k-3) +(\mu -3) j +5 (\mu -6) k$
$\therefore [(-3\mu -3) \hat i +(\mu -3) \hat j +( 5 \mu -6) \hat k ], (\hat i - 4 \hat j +3 \hat k]= -3 \mu -3 -4 \mu +12+15 \mu -18=0$
$8 \mu -9=0$
$\mu =\large\frac{9}{8}$