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

1.	Find the angles between each of the following pairs of straight lines : 3x + 4y – 7 = 0 and 4x – 3y + 5 = 0
Answer» 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. m₁ = \(-\frac{3}{4}\) ,m₂ = \(\frac{4}{3}\) ∵m₁m₂ = \(-\frac{3}{4}\times\frac{4}{3}=-1\) 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 + 4y – 7 = 0 and 4x – 3y + 5 = 0

Answer»

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.

m₁ = \(-\frac{3}{4}\) ,m₂ = \(\frac{4}{3}\)

∵m₁m₂ = \(-\frac{3}{4}\times\frac{4}{3}=-1\)

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