given L1:2x-3y=-1 and L2:5x+y=2 find the angle between these lines?

Answer 1

First calculate the slopes of both lines.

The angle of each line from the positive x-axis is the tangent of the slope.

m1 = tanβ = 2/3
m2 = tanα = -5

The angle between the lines is:

γ = α - β

Use the tangent subtraction formula.

tanγ = tan(α - β) = (tanα - tanβ) / [1 + (tanα)(tanβ)]
tanγ = (-5 - 2/3) / [1 - (-5)(2/3)] = (-17/3) / (-7/3) = 17/7

γ = arctan(17/7) ≈ 67.6°

Answer 2

2 ways..compute the arctan(2/3) and arctan (-5)and add them together...will be a negative angle...period of tan function is pi...thus add pi to your result ...or do tan (a -b) = [tan a - tan b] / [1 + tan a tan b]...minus sign since b is in ( - pi / 2 , 0]