Question

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

• A. $0$
• B. $1$
• C. $\frac{3}{2}$
• D. $-\frac{5}{2}$

Answer 1

The correct option is D $-\frac{5}{2}$

If $\overrightarrow{a}$ and $\overrightarrow{b}$ is orthogonal, then $\overrightarrow{a}.\overrightarrow{b}=0$

$\Rightarrow (2\hat{i}+\lambda \hat{j}+\hat{k}).(\hat{i}+2\hat{j}+3\hat{k})=0$

$\Rightarrow 2+2\lambda +3=0$

$\Rightarrow \lambda =-\frac{5}{2}$