Question

Find the angle between the lines $3x+y-7=0$ and $x+2y-9=0$ ?

Answer 1

Equation of lines is given as:

$3x+y-7=0\Rightarrow y=-3x+7where,m_1=-3and,x+2y-9=0\Rightarrow y=-\frac{x}{2}+\frac{9}{2}where,m_2=-\frac{1}{2}$

angle between the lines is given by;

$\tan \theta =\left|\frac{m_2-m_1}{1-m_1{m}_2}\right|\Rightarrow \tan \theta =\left|\frac{-\frac{1}{2}-(-3)}{1-(-\frac{1}{2})(-3)}\right|\Rightarrow \tan \theta =1\Rightarrow \theta =\frac{\pi }{4}$