Question

Find the angle between the lines $x=a$ and $by+c=0$

Answer 1

$x=a$

$\Rightarrow m_1=\frac{1}{0}$

$by+c=0$

$y=\frac{-c}{b}$

$m_2=0$

Comparing with $y=mx+c$

Then, putting in

$tan\theta =\left|\frac{m_1-m_2}{1+m_1{m}_2}\right|$

$=\left|\frac{\frac{1}{0}-0}{1+\frac{1}{0}\times 0}\right|$

$=\frac{1}{0}=\infty$

$\Rightarrow \theta ={90}^{\circ }$