How are direction cosines defined for a position vector OP in vector analysis?

Direction cosines for a position vector OP are defined as the cosines of the angles that OP makes with the three coordinate axes. Specifically, if OP is represented as OP = r = ai + aj + ak, the direction cosines are given by cos(α), cos(β), and cos(γ), where α, β, and γ are the angles between OP and the x, y, and z axes, respectively.