Direction Cosines are the Cosines Of the Angles of the angles between and the line and the coordinate Axis. If we have a vector (a,b,c) in space then two a=x2-x1,b=y2-y1 and c =z2-z1 are called the direction ratio of the line.
Whereas
Cos alpha = a/( a^2+b^2+c^2)^1/2
Cos beta =b/( a^2+b^2+c^2)^1/2
Cos gamma =c/( a^2+b^2+c^2)^1/2
Cos alpha, cos beta and Cos gamma are called the direction ratios of a line and alpha, beta and gamma are called the angle made by the line with x, y, z-axis respectively.