Final answer:
The lines l1 and l2 have direction vectors that are not proportional, indicating that the lines are not parallel. They also do not share a common point and therefore do not intersect, meaning they are skew lines.
Step-by-step explanation:
To determine if the lines l1: x-8=-t, y-7=2t, z-3=2t and l2: x-6=s, y-9=-s, z-8=2s are parallel or intersect, we must compare their direction vectors. For l1, the direction vector is (-1, 2, 2), and for l2, it is (1, -1, 2). These vectors are not proportional to each other, therefore the lines are not parallel.
Next, we would check if the lines intersect by setting up a system of equations to find a common solution for t and s that satisfies all three coordinate equations given by l1 and l2. However, because the direction vectors are not parallel and not opposite, and there is no point that exists on both lines, we can conclude that the lines are neither parallel nor do they intersect; thus, they are skew lines.