The two lines ax + by = c and a′x + b′y = c′ are perpendicular if - Vidyadip

MCQ

The two lines ax + by = c and a′x + b′y = c′ are perpendicular if

A
ab′ = ba′
B
aa′ + bb′ = 0
C
ab + a′b′ = 0
D
ab′ + ba′ = 0

✓

Answer

(b) $aa ^{\prime}+ bb ^{\prime}=0$
Explanation: We know that Slope of the line $a x+b y=c$ is $\frac{-a}{b}$, and the slope of the line $a^{\prime} x+b^{\prime} y=c^{\prime}$ is $\frac{-a^{\prime}}{b^{\prime}}$ The lines are perpendicular if $\tan \theta=\frac{3}{5-x}$ (1)
$\frac{-a}{b} \frac{-a^{\prime}}{b}=-1 \text { or } a a^{\prime}+b b^{\prime}=0$

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