Find the angle between the lines x = a and by + c = 0. - Vidyadip

Question

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

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Answer

$\text{x}=\text{a}$ $\Rightarrow\text{m}_1=\frac{1}{0}$ $\text{by}+\text{c}=0$ $\text{y}=\frac{-\text{c}}{\text{b}}$ $\text{m}_2=0$ Comparing with y = mx + c Then, putting in $\tan\theta=\Big|\frac{\text{m}_1-\text{m}_2}{1+\text{m}_1\text{m}_2}\Big|$ $=\Bigg|\frac{\frac{1}{0}-0}{1+\frac{1}{0}\times0}\Bigg|$ $=\frac{1}{0}=\infty$ $\Rightarrow\theta=90^\circ$

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