Given two lines $L_{1} a n d L_{2}$ are such that $L_{1}$ passes through the point $(2018, 2019, 2020)$ and $L_{2}$ passes through the point $(2019, 2020, 2021)$ . If the direction cosines of both lines will satisfy the given relations $l + m + n = 0$ and $l^{2} + m^{2} - n^{2} = 0$ . If $θ$ is angle between the lines $L_{1} a n d L_{2}$ , then the possible value(s) of $\cos θ$ is/are ___ (for skew lines, angle between them means angle between their direction ratios)

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$\frac{- 1}{2}$

$- \frac{\sqrt{3}}{2}$

$1$

$\frac{1}{2}$

answer is A, C, D.

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Detailed Solution

$l + m + n = 0 l^{2} + m^{2} = n^{2} l^{2} + m^{2} + 2 l m = n^{2} l m = 0$

$l = 0 o r m = 0 0, m, - m o r l, o, - l$

dr’s can be $0, 1, - 1 (O R) 1, 0, - 1$
$\cos θ = \frac{1}{2} θ = 60^{\circ} (O R) 0^{\circ}$
Lines can be parallel also.

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