You can
put this solution on YOUR website!in vectors, we tend to discuss problems in 3-d space and we think of the 3 axes, x, y and z.
However, in true abstract thought, we should not think about the 3 axes, since some questions are not spatial questions. So what do we base our vectors on then? We tend to pick basic vectors, eg (1,0) and (0,1), for a 2-d example. These are your bases.
So, a basis is a building block for your vectors. They do not need to be perpendicular to each other (whatever that implies in non-spatial questions) - but usually are perpendicular, but they should definitely not be parallel to each other.
Hope this helps?
Jon.
