Question

Why must our cordinate systems have perpendicular axes?

Answer 1

There is no hard and fast rule that the coordinate systems to have perpendicular axes. You can make your own coordinate axes which may or may not be perpendicular to each other. If they are the not perpendicular to each other, the calculations become really hard and tough to solve and also finding coordinates leads to relatively long computations. The whole vector algebra is made simple by considering perpendicular axes, if they are not perpendicular then the problems would become tough to solve. It is a general idea to assume perpendicular coordinate systems.