Answer
Since the lines share at least one point and the lines are parallel, the lines are coincident.
Work Step by Step
When $n=1$, line 1 passes through the point $(1,2,-3)$. Line 2 also passes through this point when $r=0$. Therefore, the lines have at least one point in common.
A direction vector for line 1 is $(1,2,-3)$ and a direction vector for line 2 is $(-1,-2,3)$. When $n=-1$, the product of $n$ and the direction vector of line 1 is equal to the direction vector of line 2. Therefore, the lines are parallel.
Since the lines share at least one point and the lines are parallel, the lines are coincident.
