Question

acute angle between the lines 3x-y-4=0 and 2x+y-3=0
​

Answer 1

Answer:

θ = tan⁻¹($\frac{1}{7}$)

Step-by-step explanation:

property used:

If θ is the angle between two intersecting lines defined by y₁= m₁x₁+c₁ and y₂= m₂x₂+c₂, then, the angle θ is given by

tanθ=±(m₂-m₁) / (1+m₁m₂)

line1 => 3x-y-4= 0  => y = 3x-4

line2 => 2x+y-3=0​​ => y = -2x+3

here,

m₁ = 3 , m₂ = -2

=> tanθ = $\frac{| 3 -2 |} {1+(3*2)}$

            =  $\frac{| 1 |}{1+6 }$ = $\frac{1}{7}$

           

here, tanθ = $\frac{1}{7}$

=> θ = tan⁻¹($\frac{1}{7}$)