Question

The angle between the lines whose direction cosines satisfy the equations l + m + n = 0, 2lm+2ln-mn=0 is

• A. ${30}^{\circ }$
  
• B. ${120}^{\circ }$
  
• C. ${45}^{\circ }$
  
• D. ${150}^{\circ }$
  

Answer 1

The correct option is B ${120}^{\circ }$


$l+m+n=0\Rightarrow l=-(m+n)$
$2l(m+n)-mn=0\Rightarrow 2(m+n{)}^2+mn=0$
$\Rightarrow 2m^2+5mn+2n^2=0$
$\Rightarrow m+2n=0$ or 2m+n=0
$\therefore$ DRS are (1,-2,1), (1,1,-2) cos $\theta =-\frac{1}{2}\Rightarrow \theta ={120}^{\circ }$