Find the angle between the lines y - 3x + 2 = 0 and 9x = 3y + 7 .

Question

Question

Answer 1

Concept :

The angle θ between the lines having slope m₁ and m₂ is given by,

\(\rm \tan θ = \left | \frac{m_{1}-m_{2}}{1+m_{1}m_{2}} \right |\)

Calculation :

We have given equation of lines are, y - 3x + 2 = 0 and 9x = 3y + 7

⇒ y = 3x - 2

⇒ m₁ = 3 ____( i )

and , 3y = 9x - 7

⇒ y = 3x - 7/3

⇒ m₂ = 3 ____( ii )

We know that , \(\rm tanθ = \left | \frac{m_{1}-m_{2}}{1+m_{1}m_{2}} \right |\)

⇒ tan θ = \(\rm\left | \frac{3-3}{1+9} \right |\)

⇒ tan θ = 0

⇒ θ = 0 .

The correct option is 3.

Additional Information

The slopes of parallel lines are equal.

If lines are parallel then angle θ between the lines is zero.