Find the direction cosine of a line which makes equal angles
with the co-ordinate axes.

Answer

Let `alpha` be the common inclination of the line with the three axes then the d.c.'s of the line are `cosalpha, cosalpha, cosalpha`
If l, m, n are the d.c.'s of a line then `l^2+m^2+n^2=1`
`therefore cos^2alpha+cos^2alpha+cos^2alpha = 1`
`3cos^2alpha = 1`
`cos^2alpha=(1)/3 => cosalpha=pm(1)/sqrt5
Thusm the d.c.'s of line are `pm(1)/sqrt3, pm(1)/sqrt3, pm(1)/sqrt3,`