Q102 / 180 · KCET 2020 · Mathematics

The two lines $l x+m y=n$ and $l^{\prime} x+m^{\prime} y=n^{\prime}$ are perpendicular if

  • Correct answer
    A
    $l l^{\prime}+m m^{\prime}=0$
  • B
    $l m^{\prime}+m l^{\prime}$
  • C
    $l m+l^{\prime} m^{\prime}=0$
  • D
    $l m^{\prime}+m l^{\prime}=0$

Solution

Given lines $l x+m y=n$ and $l^{\prime} x+m^{\prime} y=n^{\prime}$ Slope of line $l x+m y-n=0$ is $-l / m$ and slope of line $l^{\prime} x+m^{\prime} y-n^{\prime}=0$ is $-l^{\prime} / m^{\prime}$ lines are perpendicular $\begin{aligned} \therefore \quad\left(\frac{-l}{m}\right)\left(\frac{-l^{\prime}}{m^{\prime}}\right) &=-1 \\ l l^{\prime}+m m^{\prime} &=0 \end{aligned}$

Hence, the correct answer is option: 'A'.

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