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Q.

The acute angle between the two lines whose dc’s are given by $l + m - n = 0$ and $l^{2} + m^{2} - n^{2} = 0$ is

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a

0

b

$\frac{π}{6}$

c

$\frac{π}{4}$

d

$\frac{π}{3}$

answer is D.

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Detailed Solution

$\begin{array}{l} l^{2} + m^{2} - {(l + m)}^{2} = 0 \Rightarrow l m = 0 \\ m = 0 \Rightarrow l = n \Rightarrow l : m : n = 1 : 0 : 1 \\ l = 0 \Rightarrow m = n \Rightarrow l : m : n = 0 : 1 : 1 \\ \cos θ = \frac{0 .1 + 1 .0 + 1 .1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2} \Rightarrow θ = \frac{π}{3} \end{array}$

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