Question

If a line lies in the octant $OXYZ$ and it makes equal angles with the axis, then

• A. $l=m=n=\frac{1}{\surd 3}$
• B. $l=m=n=\pm \frac{1}{\surd 3}$
• C. $l=m=n=-\frac{1}{\surd 3}$
• D. $l=m=n=\pm \frac{1}{\surd 2}$

Answer 1

The correct option is A

$l=m=n=\frac{1}{\surd 3}$

Explanation for the correct option:

Given, line makes equal angles with the Coordinate axis

$\therefore l=m=n$

As we know,

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

$\Rightarrow$ $3l^2=1$

$\Rightarrow$ $l^2=\frac{1}{3}$

$\Rightarrow$ $l=\frac{1}{\sqrt{3}}$

$\mathbf{\therefore }\left(l=m=n\right)\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{\sqrt{\mathbf{3}}}$

Hence, option ‘A’ is Correct.