What are the direction cosines of a line which is equally inclined to the axes?

Options

A. `(: 1/sqrt3,1/sqrt3,1/sqrt3 :)`
B. `(: -1/sqrt3,1/sqrt3,1/sqrt3 :)`
C. `(: -1/sqrt3,-1/sqrt3,1/sqrt3 :)`
D. `(: 1/3,1/3,1/3 :)`

Answer

A

Explanation

Let l,m,n are the dc's of a line that is inclined equally at `alpha` to the +ve direction of axes.
Now, `l=cosalpha`
`m=cosalpha`
`n=cosalpha`
Also, `l^2+m^2+n^2=1`
`3cos^2alpha=1`
`cosalpha=1/sqrt3`
`:." dc's of the line are": (: 1/sqrt3,1/sqrt3,1/sqrt3 :)`