Question

The acute angle between two lines whose direction cosines are given by the relation between $l+m+n=0and{l}^2+m^2-n^2=0$

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $noneofthese$

Answer 1

The correct option is B $\frac{\pi }{3}$

$l+m+n=0...\left(i\right)l^2+m^2-n^2=0...\left(ii\right)FromEqs.\left(i\right)and\left(ii\right)l^2+m^2-(-l-m{)}^2=0lm=0\therefore l=0orm=0CaseI:If,l=0Then,m+n=0\therefore \frac{l}{0}=\frac{m}{-1}=\frac{n}{1}=\frac{1}{\sqrt{2}}CaseII:If,m=0Then,l+n=0\therefore \frac{l}{0}=\frac{m}{0}=\frac{n}{1}=\frac{1}{\sqrt{2}}$
If angle between lines is $\theta$
$\therefore cos\theta =0+0+\frac{1}{2}\therefore \theta =\frac{\pi }{3}$