Direction cosines (l, m, n) of a line are cosines of angles the line makes with x, y, z axes. They satisfy $l^{2}$ + $m^{2}$ + $n^{2}$ = 1. Direction ratios (a, b, c) are any set of numbers proportional to direction cosines: l = a/sqrt($a^{2}$+$b^{2}$+$c^{2}$), etc. A line has unique DCs (up to sign) but infinitely many sets of DRs. For a line joining P(x_{1},y_{1},z_{1}) and Q(x_{2},y_{2},z_{2}), DRs are (x_{2}-x_{1}, y_{2}-y_{1}, z_{2}-z_{1}). Important: DCs of the coordinate axes are (1,0,0), (0,1,0), (0,0,1). If DRs of a line are (a,b,c), the DCs are ±(a,b,c)/sqrt($a^{2}$+$b^{2}$+$c^{2}$).