Find the angles between each of the following pairs of straight lines :
3x – y + 5 = 0 and x – 3y + 1 = 0
Given:
The equations of the lines are
3x − y + 5 = 0 … (1)
x − 3y + 1 = 0 … (2)
To find:
Angles between two lines.
Explanation:
Let m1 and m2 be the slopes of these lines.
m1 = 3, m2
Let θ be the angle between the lines.
Then,
⇒
Hence, the acute angle between the lines is