Question

If the direction cosine $l,m,n$ of a line are related by the equations $l+m+n=0,2ml+2mn=0$ then the ordered triplet $(l,m,n)$ is

• A. $\left(\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{-2}{\sqrt{6}}\right)$
• B. $\left(\frac{-1}{\sqrt{6}},\frac{-1}{\sqrt{6}},\frac{-2}{\sqrt{6}}\right)$
• C. $\left(\frac{-2}{\sqrt{6}},\frac{1}{\sqrt{6}},\frac{1}{\sqrt{6}}\right)$
• D. None

Answer 1

The correct option is D None

We know that $l^2+m^2+n^2=1$

Given $l+m+n=0$

$2ml+2mn=0$

$l=-n$

$m=0$

$2l^2=1$

$l=\frac{1}{\sqrt{2}},m=0,n=\frac{-1}{\sqrt{2}}$

$D$ is correct $(\frac{1}{\sqrt{2}},0,\frac{-1}{\sqrt{2}})$ or $(\frac{-1}{\sqrt{2}},0,\frac{1}{\sqrt{2}})$