Question

Two lines are represented by equations $x+y=1$ and $x+ky=0$are mutually orthogonal if $k$ is

• A. $1$
• B. $-1$
• C. $0$
• D. None of these

Answer 1

The correct option is B

$-1$

Find the value of $K$:

Let the slope of the line $x+y=1$ be $m_1=-1$

Let the slope of the line $x+ky=0$be $m_2=\frac{-1}{k}$

Now, for perpendicular lines $=m_1\times m_2=-1$

$$\begin{gathered} \Rightarrow -1\times \frac{-1}{k}=-1 \\ \Rightarrow k=-1 \end{gathered}$$

Hence, the correct option is (B).