Well, I'm not an expert on the subject but... Thinking about it, I believe you could both use it offensively and defensively.
Thinking of it in an offensive way, you could potentially stop your enemy's attack via the vectors said attack may have. Though maybe due to limitations that could be difficult, since it could only affect attacks that were indeed physical, and not perhaps fire, gases and stuff. You could then direct the enemy's attack towards them, essentially reflecting the opponent's attack on themselves. Other way is to simply take advantage of your surroundings and use everyday objects to your offense... Let's say, maybe rocks, debris, or something more crazy? Since vectors affect momentum and position you could direct it to the enemy faster than they could perhaps pull it off.
In defense, maybe in theory (?) you could create a vector shield using nearby vectors, essentially (once again) reflecting the opponent's attack. Another way would be to simply use your own vectors to perhaps dodge an attack?
Again, I'm no expect and certainly not really acquainted with powers that envolve things such as physics lol. To me, Vector Manipulation is just a more intellectual and organized way of view telekinesis, but I could be wrong. I'm just trying to think this as something that could happen in a tv show.
Hope I helped anyhow!
You can use to act on anything so long as it can be perceived as having both a size and direction. Since direction relates to space, this essentially allows you to control anything related to how much motion (change in position) something has in a given direction (path in space).