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°

Answer 1

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°