Question

The slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3 , find the slopes of the lines.

Answer 1

Solution:
Let the slopes of the two given lines be m and 2m and θ be the angle between them

The according to questions

or 1 + 2m² = 3m

or 2m² - 2m + 1= 0

or 2m² - 2m -m + 1= 0

or 2m(m – 1) – 1(m – 1) = 0

or (m – 1) (2m – 1) = 0