Elementary Problem on Coordinates

Question

If I invented a coordinate system of 3 parameters - just like in Cartesians $(x,y,z)$, should those 3 parameters have directional vectors that are mutually perpendicular?

Answer 1

A basis will not, in general, be orthogonal, however, given any basis, you can produce an orthogonal basis. Having an orthogonal basis can be quite useful, but it is not necessary.