How to make vector graphic based video games?

Bun

For example : Vector Runner
http://www.digyourowngrave.com/vector-runner

the vector style im referring to is that of the 1980s also used in many old arcade games such as Tempest, Battlezone, Red baron, Black Widow etc
Also this http://www.digyourowngrave.com/vector-conflict-the-siege/

Answer
XNA Game Studio allows you to make a wide dynamic of game including vector-based.

http://msdn.microsoft.com/en-us/library/bb200104.aspx

An example(based off of geometry wars)
http://www.youtube.com/watch?v=NZcJZ-_FIO4

vector addition and subtraction?

Answer
I cannot give you info in here because vectors deals with figures, so I am giving you the following links.

http://btc.montana.edu/olympics/physbio/physics/kin09.html

http://physics.info/vector-addition/

http://www.maths.usyd.edu.au/u/MOW/vectors/vectors-3/v-3.html

If you have gathered the right concepts, then here is an interesting game for you:

http://www.cut-the-knot.org/Games/Vectors.shtml

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