Question

what is orthonormal ?
whats its applications?

Answer 1

ortho = perpendicular
normal = normalized, usually to length 1

Answer 2

orthonormal axes are commonly used in science and engineering as reference frames (to give one example)

Answer 3

in fact, orthonormal axes provide the frame in which ordinary "x-y plane" problems are done in math; x and y are perpendicular, and the units of measurement are all relative to the vectors from the origin to (1,0) and from the origin to (0,1).

Answer 4

those two vectors (from the origin to (1,0) and from the origin to (0,1)) are orthonormal.