Question

Find the condition, if the two lines ax + by = c and a′x + b′y = c′ are perpendicular.

Answer 1

The given lines are 

ax + by = c ⇒ y = \(-\frac{ax}{b}+\frac{c}{b},m_1=-\frac{a}{b}\) 

and a'x +b'y = c' ⇒ y = \(\frac{a'}{b'}x+\frac{c'}{b'},m_2=-\frac{a'}{b'}\) 

Since the line are perpendicular. 

∴ m₁m₂ = – 1 

⇒ (−\(\frac{a}{b}\) ) (−\(\frac{a'}{b'}\)) = − 1 

⇒ \(\frac{aa'}{bb'}=-1\) 

⇒ aa′ + bb′ = 0, which is the required condition.