The dot product is one of those elusive things that you aren't taught soon enough (In my opinion). If you want to do any lighting calculations yourself, then the dot product will be used extensively for diffuse calculations.
Vectors are the back bone of 3D graphics, without them, the world of computer graphics would be a very messy place. And knowing the length of them often comes in handy, especially when looking at intersections and collisions.
Lines, who doesn't love lines. They start at one point and end at another. In fact, lines are essential. What makes up a triangle? 3 lines. How do we draw a circle? A lot of lines. Knowing about them would be a good idea :)