Angle Between Two Lines

Angle between two lines :

Let two line y = m₁x + c₁  and  y = m₂x + c₂  and intersect at point A and makes an angle θ.

Where m₁ = tana

and

m₂ = tanβ,

then angle between two lines is –

θ = a  β

  1.  
angle between two lines
    1. If m₁  = m₂

Both lines are parallel to each other.

θ = 0

          2. If m₁m₂ = -1 

Both lines are parallel to each other.

θ = 90

Two given line –

L₁ ::   a₁x + b₁y + c₁ = 0   and

L₂ ::  a₂x + b₂y + c₂ = 0 

Parallel Test :

If a₁ : a₂ = b₁ : b₂ ( both slope are equal m₁ = m₂ )

Perpendicular Test :

If a₁a₂+ b₁b₂ = 0 ( m₁m₂ = -1 )

Identical Test :

a₁ : a₂= b₁:b₂ = c₁:c₂

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