The vectors vec(a) and vec(b) have lengths 2 and 1, respectively. The vectors vec(a)+5vec(b) and 2vec(a)-3vec(b) are perpendicular. Determine the angle between vec(a) and vec(b).

A) Find the dot product of vec(a) and vec(b)
B) Use the Pythagorean theorem to find the magnitude of vec(a)
C) Calculate the cross product of vec(a) and vec(b)
D) Use the cosine formula to find the angle between vec(a) and vec(b)