The lines $\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$ and $\frac{x-3}{-3}=\frac{y-4}{-6}=\frac{z-5}{-9}$ are :

parallel

The correct answer is Option (4) → parallel

$l_1:\frac{x}{1}=\frac{y}{2}=\frac{z}{3}$

$l_2:\frac{x-3}{-3}=\frac{y-4}{-6}=\frac{z-5}{-9}$

$\vec{v_1}||l_1=\hat i+2\hat j+3\hat k$

$\vec{v_2}||l_2=-3(\hat i+2\hat j+3\hat k)$

as $\vec{v_2}=-3\vec{v_1}$

$⇒v_1||v_2⇒l_1||l_2$