The direction cosines of a line are $l$, $m$, $n$. They satisfy:

Direction cosines are the cosines of the angles that a line makes with the three coordinate axes: $l = \cos\alpha$, $m = \cos\beta$, $n = \cos\gamma$. Key identity: $l^2 + m^2 + n^2 = \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1$. This just says the unit vector along the line has unit length when projected onto the three axes.