Q1 of 319 Page 24

Find the angles between each of the following pairs of straight lines :
3x + 4y – 7 = 0 and 4x – 3y + 5 = 0

Given:

The equations of the lines are

3x + 4y − 7 = 0 … (1)

4x − 3y + 5 = 0 … (2)

To find:

Angles between two lines.

Explanation:

Let m₁ and m₂ be the slopes of these lines.

m₁m₂

∵m₁m₂

Hence, the given lines are perpendicular.
Therefore, the angle between them is 90°.

Find the angles between each of the following pairs of straight lines :

3x + y + 12 = 0 and x + 2y – 1 = 0

Find the angles between each of the following pairs of straight lines :

3x – y + 5 = 0 and x – 3y + 1 = 0

Find the angles between each of the following pairs of straight lines :

x – 4y = 3 and 6x – y = 11

Find the angles between each of the following pairs of straight lines :

(m² – mn) y = (mn + n²)x + n³ and (mn + m²)y = (mn – n²)x + m³.

Find the angles between each of the following pairs of straight lines :3x + 4y – 7 = 0 and 4x – 3y + 5 = 0