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If the DC's of two lines are given by $l + 3 m + 5 n = 0$ and $5 l m - 2 m n + 6 l n = 0$ then the angle between the lines is

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$\cos^{- 1} (\frac{1}{6})$

$\cos^{- 1} (\frac{1}{5})$

$\cos^{- 1} (\frac{1}{3})$

$\sin^{- 1} (\frac{1}{6})$

answer is A.

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Detailed Solution

$l + 3 m + 5 n = 0 \Rightarrow l = - 3 m - 5 n$

$5 l m - 2 m n + 6 \ln = 0$

$\Rightarrow m^{2} + 3 m n + 2 n^{2} = 0$

$m (m + 2 n) + n (m + 2 n) = 0$

$\Rightarrow m = - n, m = - 2 n$

(2,1,-1),(1,-2,1)

$\cos θ = \frac{1}{6} \Rightarrow θ = \cos^{- 1} (\frac{1}{6})$

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