Question

If a line makes angles of 90°, 60° and 30° with the positive direction of x, y, and z-axis respectively, find its direction cosines.

Answer 1

Let the direction cosines of the line be l, m, n.

Now,

$$\begin{gathered} l=\cos {90}^0=0 \\ m=\cos {60}^0=\frac{1}{2} \\ n=\cos {30}^0=\frac{\sqrt{3}}{2} \\ \mathrm{Therefore},\mathrm{the}\mathrm{direction}\mathrm{cosines}\mathrm{of}\mathrm{the}\mathrm{line}\mathrm{are}0,\frac{1}{2},\frac{\sqrt{3}}{2}. \end{gathered}$$