Answer
Since there is a real number $n$ such that the product of $n$ and a direction vector for line 1 is equal to a direction vector of line 2, the two lines are parallel.
Work Step by Step
A direction vector for line 1 is $(1,2,-3)$
A direction vector for line 2 is $(-1,-2,3)$
Note that $(-1) \cdot (1,2,-3) = (-1,-2, 3)$
Since there is a real number $n$ such that the product of $n$ and a direction vector for line 1 is equal to a direction vector of line 2, the two lines are parallel.
