If the direction cosines of two lines are given by $l + m + n = 0$ and $l^{2} - 5 m^{2} + n^{2} = 0$ , then the angle between them is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{π}{6}$

$\frac{π}{4}$

$\frac{π}{3}$

$\frac{π}{2}$

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$l + m + n = 0 \Rightarrow l = - m - n l^{2} - 5 m^{2} + n^{2} = 0 \Rightarrow {(- m - n)}^{2} - 5 m^{2} + n^{2} = 0 m^{2} + n^{2} + 2 m n - 5 m^{2} + n^{2} = 0 - 4 m^{2} + 2 m n + 2 n^{2} = 0 \Rightarrow 2 m^{2} - m n - n^{2} = 0 \Rightarrow (m - n) (2 m + n) = 0 \Rightarrow m = n (o r) n = - 2 m C a s e - (1) m = n \Rightarrow l = - 2 n \Rightarrow - 2 n : n : n \Rightarrow - 2 : 1 : 1 n = - 2 m \Rightarrow l = - m + 2 m = m \Rightarrow m : m : - 2 m \Rightarrow 1 : 1 : - 2$
$\cos θ = \frac{| a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} |}{\sqrt{a_{1}^{2} + b_{1}^{2} + c_{1}^{2}} \sqrt{a_{2}^{2} + b_{2}^{2} + c_{2}^{2}}} = \frac{1}{2} = \frac{π}{3}$