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Q.

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

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a

$\frac{π}{3}$

b

$\frac{π}{4}$

c

$\frac{π}{6}$

d

$\frac{π}{2}$

answer is D.

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Detailed Solution

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$l = - (m + n)$ is sub – inis sub – in
$l^{2} = m^{2} + n^{2} \Rightarrow m n = 0$
$\Rightarrow m = 0 (0 r) n = 0$
$m = 0 \Rightarrow \frac{l}{1} = \frac{m}{0} = \frac{n}{- 1}$ $C o s θ = \frac{1}{2}$
$n = 0 \Rightarrow \frac{l}{1} = \frac{m}{- 1} = \frac{n}{0}$ $θ = 60^{0} = \frac{π}{3}$

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