Question

Find $\lambda$ if the vectors $2i+j+k$ and $i-4j+\lambda k$ are mutually perpendicular.

• A. $-6$
• B. $-2$
• C. $2$
• D. $6$

Answer 1

Answer: (C)

$2$

$2\hat{i}+\hat{j}+\hat{k}$ is perpendicular to $\hat{i}-4\hat{j}+\lambda \hat{k}$
Hence, their dot product will be 0.
So, $(2\hat{i}+\hat{j}+\hat{k}).(\hat{i}-4\hat{j}+\lambda \hat{k})=0$
$\Rightarrow 2-4+\lambda =0$
Or $\lambda =2$