Question

Find the angle between straight line 2x+3y+3=0 and 3x-2y+4=0

Answer 1

EXPLANATION.

Angle between the straight lines,

⇒ 2x + 3y + 3 = 0.

⇒ 3x - 2y + 4 = 0.

As we know that,

Slope of the line y = mx + c.

From equation (1), we get.

Slope of line : 2x + 3y + 3 = 0.

⇒ 2x + 3y + 3 = 0.

⇒ 3y = - 2x - 3.

⇒ y = -2x/3 - 3/3.

⇒ y = -2x/3 - 1.

Slope : M₁ = -2/3.

From equation (2), we get.

Slope of line : 3x - 2y + 4 = 0.

⇒ 3x - 2y + 4 = 0.

⇒ - 2y = - 3x - 4.

⇒ 2y = 3x + 4.

⇒ y = 3x/2 + 4/2.

⇒ y = 3x/2 + 2.

Slope : M₂ = 3/2.

As we know that,

⇒ tan∅ = | m₁ - m₂/1 + m₁m₂ |.

Put the values of m in  this equation, we get.

⇒ tan∅ = | - 2/3 - 3/2/1 + (-2/3)(3/2) |.

⇒ tan∅ = | -4 - 9/6/1 - 1 |.

⇒ tan∅ = | -13/9/0 |.

⇒ tan∅ = 90°.

⇒ ∅ = π/2.