Show that the distance measure defined as the angle between two data vectors, x and y, satisfies the metric axioms given on page 70. Specifically, angle between two data vectors is arccos( cos(x, y) ), so d(x, y) = arccos( cos(x, y) )Show for distance measure arccos( cos(x, y) )A) Positivity1) d(x, x) >= 0 for all x and y,2) d(x, y) == 0 onlY if x == y. B) Symmetryd(x, y) == d(y, x) for all x and y. C) Triangle Inequalityd(x, z) < d(x, y) + d(y, z) for all points x, y, and z. D) Explain in simple English the intuition for why would arccos( cos(x, y) ) satisfy the same properties (A, B,C above) as the Euclidean distance.