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Question
Find the angle between the lines y = `(2 - sqrt(3)) (x + 5)` and y = `(2 + sqrt(3))(x - 7)`
Solution
The given equations are y = `(2 - sqrt(3))(x + 5)` .....(i)
And y = `(2 + sqrt(3))(x - 7)` ...(ii)
Slope of equation (i) m1 (say) = `(2 - sqrt(3))`
And slope of equation (ii) m2 (say) = `(2 + sqrt(3))`
Let θ be the angle between the two given lines
∴ tan θ = `|(m_1 - m_2)/(1 + m_1m_2)|`
= `|(2 - sqrt(3) - 2 - sqrt(3))/(1 + (2 - sqrt(3))(2 + sqrt(3)))|`
= `|(-2sqrt(3))/(1 + 4 - 3)|`
= `|(-2sqrt(3))/2|`
= `|- sqrt(3)|`
⇒ tan θ = `sqrt(3)` or `- sqrt(3)`
∴ θ = 60° or 120°
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