I want to take on a bigger project, and some research has led me to research vectors. I'd like to know what a good starting point would be to get up to speed with vectors and their associated math.
I guess that anything that has free (rather than tile-based) movement is a good start - in fact you could deal with Breakout's ball using vectors. I would definitely start with 2d rather than 3d.
I'm in a similar position and have written something like Asteroids as a first project. Problems that can be handled with vectors include:
- player vehicle's free 2d movement
- player vehicle's rotation (and thus acceleration and firing) independent from direction of travel
- player's bullets affected by the firing vehicle's movement
- movement of asteroid fragments after a sucessful bullet hit
I have also written AI for the player vehicle; the aiming part of this must take target movement (leading) and own movement into account, which again are good vector problems.
Most physic games uses vectors. Try to start with one that you like:
- Angry birds style
- GunBound style
- Trow something as far as possible
These are just some ideas.
You are obviously interested in rendering related math. This and a lot more has been well packaged into Mathematics for Programming Computer Graphics.
This seems to be some nice article about vector maths : http://www.wildbunny.co.uk/blog/vector-maths-a-primer-for-games-programmers/
Vectors really aren't a big deal even if you're bad at math :)
They can be used in plenty of games, I suggest you choose something involving a bit of physics.