Question

The value of $k$ if the straight lines $3x+6y+7=0$ and $2x+ky=5$ are perpendicular is

• A. $1$
• B. $-1$
• C. $2$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$-1$

Consider the given equations.

$3x+6y+7=0$ $............\left(1\right)$

$Slope{m}_1=-\frac{3}{6}=-\frac{1}{2}$

$2x+ky=5$ $.............\left(2\right)$

$Slope{m}_2=-\frac{2}{k}$

Since, both lines are perpendicular

So,

$m_1{m}_2=-1$

Therefore,

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

$\frac{1}{k}=-1$

$k=-1$

Hence, option B is the answer.