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Question
Select the correct option from the given alternatives:
The angle between the line `sqrt(3)x - y - 2` = 0 and `x - sqrt(3)y + 1` = 0 is
Options
15°
30°
45°
60°
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Solution
30°
Explanation:
Here, m1 = `(-sqrt(3))/(-1) = sqrt(3)`,
m2 = `(-1)/(-sqrt(3)) = 1/sqrt(3)`
Now, tan θ = `|("m"_1 - "m"_2)/(1 + "m"_1"m"_2)|`
∴ tan θ = `|(sqrt(3) - 1/sqrt(3))/(1 + sqrt(3) 1/sqrt(3))|`
= `|(3 - 1)/(2sqrt(3))|`
= `1/sqrt(3)`
∴ θ = 30°
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