Question

If the straight lines $2x+3y-3=0$ and $x+ky+7=0$ are perpendicular, then the value of $k$ is

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $\frac{-2}{3}$
• D. $\frac{-3}{2}$

Answer 1

The correct option is C $\frac{-2}{3}$

$2x+3y-3=0$
$\Rightarrow y=\frac{-2}{3}x+1$
Slope of $2x+3y-3=0$ is $m_1=\frac{-2}{3}$
$x+ky+7=0$
$\Rightarrow y=\frac{-1}{k}x-\frac{7}{k}$
Slope of $x+ky+7=0$ is $m_2=\frac{-1}{k}$
Since the two lines are perpendicular,
$m_1\times m_2=-1$
$\Rightarrow \frac{-2}{3}\times \frac{-1}{k}=-1$
$\Rightarrow k=\frac{-2}{3}$