Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2

1.	Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0.
Answer» Given: The equations of the lines are 2x − y + 3 = 0 … (1) x + y + 2 = 0 … (2) Let m₁ and m₂ be the slopes of these lines. m₁ = 2, m₂ = -1 Let θ be the angle between the lines. Then, by using the formula tan θ = [(m₁ – m₂) / (1 + m₁m₂)] = [(2 + 1) / (1 + 2)] = 3 So, θ = tan^-1 (3) ∴ The acute angle between the lines is tan^-1 (3).

Find the acute angle between the lines 2x – y + 3 = 0 and x + y + 2 = 0.

Answer»

Given:

The equations of the lines are

2x − y + 3 = 0 … (1)

x + y + 2 = 0 … (2)

Let m₁ and m₂ be the slopes of these lines.

m₁ = 2, m₂ = -1

Let θ be the angle between the lines.
Then, by using the formula

tan θ = [(m₁ – m₂) / (1 + m₁m₂)]

= [(2 + 1) / (1 + 2)]

= 3
So,

θ = tan^-1 (3)

∴ The acute angle between the lines is tan^-1 (3).