# Game Creation with XNA/Mathematics Physics/Vectors and Matrices

## Vectors and Matrices

We need to recall some basic facts about vector and matrix algebra, especially when trying to develop 3D games. A nice introduction with XNA examples can be found in the book by Cawood and McGee. [1]

### Right Triangle

Once upon a time there was little Hypotenuse. He had two cousins: the Opposite and his sister the Adjacent. Both were usually just known by their nick names 'Sine'[2] and 'Cosine'[3]. They lived together in a right triangle close to the woods. They were related through his mother's sister, aunty Alpha. His father, who was a mathematician, used to say that:

${\displaystyle \sin \alpha ={\frac {\textrm {opposite}}{\textrm {hypotenuse}}}={\frac {a}{h}}}$
${\displaystyle \cos \alpha ={\frac {\textrm {adjacent}}{\textrm {hypotenuse}}}={\frac {b}{h}}.}$

Sometimes he also referred to uncle Tangent (who was married to aunty Alpha) and said that

${\displaystyle \tan \alpha ={\frac {\textrm {opposite}}{\textrm {adjacent}}}={\frac {a}{b}},}$

so in a sense uncle Tangent of aunty Alpha was Sine divided by Cosine. To us that didn't make any sense, but Hypotenuse's father said that was how it always was.

### References

1. S. Cawood and P. McGee (2009). Microsoft XNA Game Studio Creator’s Guide. McGraw-Hill.