[OJFord]

> one basis could, for example, be two vectors pointing North and East; another could be a vector pointing along a certain road and one perpendicular to it.

And there's no requirement that they be perpendicular is there? The second just needs 'some amount of perpendicular', North and North-East for example? Since any [n, e] can also be described as [(1-sqrt(2)*e)*n, sqrt(2)*e] in the latter. (I think that's right, but my main point is you can do it, not the particular value there, and if that's way off I'll blame the fever.)

[datascienced]

If you can walk this way / and this way | then you can do / minus | to get your orthogonal -

[OJFord]

Yes exactly.

[Jensson]

You typically want an orthonormal basis though, but yes you don't need it.