Question

The angle between two lines 3x + y - 7 = 0 and x + 2y + 9 = 0 will be
1. 60° 
2. 45° 
3. 30°
4. 90°

Answer 1

Correct Answer - Option 2 : 45° 

Given:

The angle between two lines 3x + y - 7 = 0 and x + 2y + 9 = 0 

Formula used:

Tanθ = (m₂ - m₁)/(1 + m₁m₂)

y₁ = m₁x + c  &  y₂ = m₂x + c

Calculation:

According to the question,

3x + y - 7 = 0

⇒ y = - 3x + 7

⇒ m₁ = -3

x + 2y + 9 = 0

⇒ y = -x/2 - 9/2

⇒ m₂ = - 1/2

Tanθ = (m2 - m1)/(1 + m1m2)

⇒ (-1/2 - (-3))/(1 + (-3)(-1/2))

⇒  5/3/5/3

⇒ Tanθ = 1

⇒ θ = 45^o

∴ The angle between two lines 3x + y - 7 = 0 and x + 2y + 9 = 0 will be 45^o.