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.