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)

$-\frac{2}{3}$

Answer 2

Given, $2 x+3 y-3=0$ and $x+k y+7=0$ are perpendicular.
$\therefore 2 \times 1+3 \times k=0$
$\Rightarrow k=\frac{-2}{3}$
[if $a_{1} x+b_{1} y+c_{1}=0$ and $a_{2} x+b_{2} y+c_{2}=0$ are
perpendicular, then $\left.a_{1} a_{2}+b_{1} b_{2}=0\right]$