Question

:) Find the acute angle between the lines x + 3y + 1 = 0 and 2x - y + 4 = 0.​

Answer 1

Answer:

45°

Step-by-step explanation:

Let the slope of the lines m1 =2 and m2 = 1/3​

 

And  

tanθ=∣ m1-m2/1+m1m2 ∣

= ∣ $\frac{1}{3}$ -2/1+\frac{1}{3}.2|=1

θ=45°

Answer 2

Given,

Equation of line 1: x + 3y + 1 = 0

Equation of line 2: 2x - y + 4 = 0

To Find,

The acute angle between the given lines =?

Solution,
Slope(m1) of the line 1  = -a / b

m1 = -(1 / 3)

m1 = -1/3

Similarly, Slope(m2) of the line 2 =  -a / b

m2 = -(2 / -1)

m2 = 2

From the formula of the angle between 2 lines we have,

tan θ = $|(m_1 - m_2) / (1 + m_1m_2)|$

tan θ =$|(-1/3 - 2) / (1 + (-1/3) * (2))|$

tan θ =$|(-1 - 6/3) / (3-2) / (3))|$

tan θ =$|(-7/3) / (1 / 3)|$

Tan θ =  $|- 7|$

tan θ = 7

θ = 81.8∘

θ = 82∘

Hence, the acute angle between the given lines is 82∘