Explain why the direction cosines of a line can be used as a direction vector?

Question

how are the direction cosines and direction vectors are related, how can direction cosines of a line can be used as a direction vector?

Answer 1

Imagine a box of dimensions x, y, z, with a diagonal from (0,0,0) to (x, y, z), of length L. This diagonal forms angles Ax, Ay, Az with the edges of the box that start from (0, 0, 0). Then x = L Cos(Ax), y = L Cos(Ay), and z = L Cos(Az). Get it now?