If we have 2 Orthonormal Vectors x and y, we can use them to represent...?

If we have 2 Orthonormal Vectors x and y, we can use them to represent...?



All other Vectors in a Cartesian coordinate system, where each vector is represented as 2 real numbers.

Ex: a = x_ax + y_ay

where x_a and y_a are the real Cartesian coordinates of the 2D vector a.
There are several advantages to a Cartesian coordinate system. For instance, by the Pythagorean Theorem, the length of a is:
||a|| = √xa² + ya²

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