Question

Find the angles between each of the following pairs of straight lines : x – 4y = 3 and 6x – y = 11

Answer 1

Given: 

The equations of the lines are 

x − 4y = 3 … (1) 

6x − y = 11 … (2) 

To find: 

Angles between two lines. 

Explanation: 

Let m₁ and m₂ be the slopes of these lines. 

m₁ = \(\frac{1}{4}\), m₂ = 6 

Let θ be the angle between the lines. Then,

Hence, the acute angle between the lines is tan^-1 \(\Big(\frac{23}{10}\Big)\)