Question

Derive an expression for acute angle between two lines slopes m1 and m2 and hence find the angle between lines√3x+y=1 and x+√3y=1​

Answer 1

Answer:

30°

Step-by-step explanation:

m₁ = Tanθ₁

m₂ = Tanθ₂

Tan (θ₂ - θ₁)  =  | (Tanθ₂ - Tanθ₁)/(1 +Tanθ₂Tanθ₁) |

=> 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°