I think this is a really interesting question. I think that we could create a system of equation that would prove that the two lines are parallel but I am not entirely sure. Anyone knows how to tackle this question?
What can you conclude about the lines $$\frac{x − x_0}{a_1} = \frac{y − y_0}{a_2} = \frac{z − z_0}{a_3} \quad\text{and}\quad \frac{x − x_0}{b_1} = \frac{y − y_0}{b_2} = \frac{z − z_0}{b_3}$$
given that $a_1b_1 + a_2b_2 + a_3b_3 = 0$?