Question

The angle between two lines 3x-y +4=0 and 2x+y -3=0 is​

Answer 1

Answer:

45°  or   135°

Step-by-step explanation:

If the angle between them is θ, then,

tanθ = | (m₁ - m₂)/(1 + m₁m₂) |,  where m₁ and m₂ is the slope of the given lines.

For the slope of lines, we use y = mx + c in which m is the slope of a line.

For line 3x - y + 4 = 0:

⇒ y = 3x + 4        , slope = m₁ = 3

For line 2x + y - 3 = 0:

⇒ y = - 2x +3      , slope = m₂ = - 2

 ∴  tanθ = | {3 - (-2) }/{1 + (3)(-2)} |

              = | 5/(-5) | = | - 1 |

⇒ tanθ = 1

⇒ tanθ = tan45°

⇒ θ = 45°

          ∴ Angle between the lines is 45°

Moreover, angle can be 180° - 45° = 135°