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

Answer: (C)

$\frac{-2}{3}$

Concept: Slope of general equation of line $ax+by+c=0$ is $m=-\frac{\text{coefficient of x}}{\text{coefficient of y}}$

Therefore,

Slope of line $2x+3y-3=0$ is $=-\frac{2}{3}$

and slope of line $x+ky+7=0$ is $-\frac{1}{k}$

Now we know that two lines are perpendicular if their product of slopes is $-1$

$\Rightarrow -\frac{2}{3}\times -\frac{1}{k}=-1$

$\Rightarrow k=-\frac{2}{3}$