Question

For what value of $\lambda$ are the vectors $\lambda \hat{i}+(1+\lambda )\hat{j}+(1+2\lambda )\hat{k}$ and $(1-\lambda )\hat{i}+\lambda \hat{j}+2\hat{k}$ perpendicular?

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

Answer 1

Answer: (A)

$\frac{-1}{3}$

for perpendicular vectors

$\overrightarrow{a}.\overrightarrow{b}=0$

$\Rightarrow \lambda (1-\lambda )+\lambda (1+\lambda )+2(1+2\lambda )=0$

$\Rightarrow 6\lambda =-2$

$\Rightarrow \lambda =\frac{-1}{3}$