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 + c2 = 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