## Elementary Geometry for College Students (6th Edition)

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.
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.