Question

$\text{If}\overrightarrow{a}=3\hat{i}+\lambda \hat{j}-\hat{k}$ and $\overrightarrow{b}=\hat{i}-5\hat{j}+2\hat{k}$ are orthogonal, then the value of $\lambda$ is

• A. $1$
• B. $-1$
• C. $\frac{1}{5}$
• D. $\frac{-2}{5}$

Answer 1

The correct option is C $\frac{1}{5}$

$\overrightarrow{a}$ and $\overrightarrow{b}$ are orthogonal.
$\Rightarrow \overrightarrow{a}\cdot \overrightarrow{b}=0$
$\Rightarrow 3-5\lambda -2=0$
$\Rightarrow \lambda =\frac{1}{5}$