Question

If the direction ratios of two lines are given by $3lm-4ln+mn=0$ and $l+2m+2n=0$, then, the angle between the lines is

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (A)

$\frac{\pi }{2}$

By solving two equations we get
$(l_1,m_1,n_1)=(2\sqrt{2}-3,-\sqrt{2},1)$
$(l_2,m_2,n_2)=(-2\sqrt{2}-2,\sqrt{2},1)$
$l_1{l}_2+m_1{m}_2+n_1{n}_2=0$
Therefore, the angle between them is $\frac{\pi }{2}$.