Question

The value of $\lambda$ for which the two vectors $\overrightarrow{a}=5\hat{i}+\lambda \hat{j}+\hat{k}$ and $\overrightarrow{b}=\hat{i}-2\hat{j}+\hat{k}$ are perpendicular to each other is

• A. $2$
• B. $-2$
• C. $3$
• D. $-3$

Answer 1

The correct option is C $3$

For two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ to be perpendicular, $\overrightarrow{a}.\overrightarrow{b}=0$.

Thus, $(5\hat{i}+\lambda \hat{j}+\hat{k}).(\hat{i}-2\hat{j}+\hat{k})$

$=5(\hat{i}.\hat{i})-2\lambda (\hat{j}.\hat{j})+1(\hat{k}.\hat{k})$

$0=5-2\lambda +1$

$\Rightarrow 0=6-2\lambda \Rightarrow \lambda =3$