derive and expression for the angle between two lines y=m1x+c1 and y=m2x+c2 and hence find the angle between lines√3x+y=1 and x+√3y=1
Answers
Given : angle between two lines y=m₁1x+c₁ and y=m₂x+c₂
To Find :derive an expression for the angle between two lines
the angle between lines√3x+y=1 and x+√3y=1
m₁ = Tanθ₁
m₂ = Tanθ₂
Tan (θ₂ - θ₁) = | (Tanθ₂ - Tanθ₁)/(1 +Tanθ₂Tanθ₁) |
mod is used here as angle is acute and tan in 1st quadrant is positive,
=> Tan (θ₂ - θ₁) = | (m₂ - m₁)/(1 + m₂m₁) |
√3x+y=1
=> y = - √3x + 1
=> m₁ = - √3
x+√3y=1
=> y = - x/√3 + 1/√3
=> m₂ = -1/√3
=> Tanθ = | ( -1/√3 - (-√3))/(1 + (-1/√3)( - √3)) |
=> Tanθ = | (2/√3)/(2) |
=> Tanθ = 1/√3
=> θ = 30°
angle between lines√3x+y=1 and x+√3y=1 = 30°
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Answer:
the last sentence is: we have used mod sign as the angle thetha is acute and tan thetha in first quadrant is always positive
