Question

The relation between a, b, a' and b' such that the two lines ax + by = c and a'x + b'y = c' are perpendicular is

• A. aa' - bb' = 0
• B. aa' + bb' = 0
• C. ab + a'b' = 0
• D. ab - a'b' = 0

Answer 1

Answer: (B)

aa' + bb' = 0

Answer 2

Slope of the line $ax + by = c$ is $\frac{-a}{b}$, and the slope of the line $a'x + b'y = c'$ is $\frac{-a'}{b'}$ The lines are perpendicular if $\left(\frac{-a}{b}\right)\left(\frac{-a'}{b'}\right) = - 1$ or $aa' + bb' = 0$