The direction cosines of a line equally inclined with the co-ordinate…

The correct answer is Option (3) → $\left(±\frac{1}{\sqrt{3}},±\frac{1}{\sqrt{3}},±\frac{1}{\sqrt{3}}\right)$

Let the direction cosines be $l,m,n$

Equally inclined with the three coordinate axes gives

$l=m=n$

Using property

$l^2+m^2+n^2=1$

$3l^2=1$

$l=\frac{1}{\sqrt3}$

Hence

$l=m=n=\frac{1}{\sqrt3}$

The direction cosines are $\left(\frac{1}{\sqrt3},\frac{1}{\sqrt3},\frac{1}{\sqrt3}\right)$.