Question

Find the direction cosines of a line which makes equal angle with the coordinate axes.

Answer 1

Let the direction cosines of the line make an angle α with each of the coordinate axes.
∴l=cosα,m=cosα,n=cosα
l2+m2+n2=1
⇒ cos2α+cos2α+cos2α=1
⇒ 3cos2α=1
⇒ cos2α=$\frac{1}{3}$
⇒ cosα=±$\frac{1}{\sqrt 3}$
Thus,the direction cosines of the line, which is equally inclined to the coordinate axes,
are ±$\frac{1}{\sqrt 3}$,±$\frac{1}{\sqrt 3}$and±$\frac{1}{\sqrt 3}$.