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

The lines intersect at the point $(2,3,4)$
When $n=0$, line 1 passes through the point $(2,3,4)$. When $r=0$, line 2 passes through the point $(2,3,4)$. Therefore, the point $(2,3,4)$ is included in each line. A direction vector for line 1 is $(1,2,-3)$ and a direction vector for line 2 is $(2,3,5)$. Since there is no real number $n$ such that the product of $n$ and the direction vector of line 1 is equal to the direction vector of line 2, the lines are not parallel. Therefore, the lines intersect at the point $(2,3,4)$