Question

The value of $[\overrightarrow{i}+\overrightarrow{j},\overrightarrow{j}+\overrightarrow{k},\overrightarrow{k}+\overrightarrow{i}]$ is equal to

• A. $0$
• B. $1$
• C. $2$
• D. $4$

Answer 1

Answer: (C)

$2$

Fact: $[\overrightarrow{a}+\overrightarrow{b}\overrightarrow{b}+\overrightarrow{c}\overrightarrow{c}+\overrightarrow{a}]=2\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]$

Here $\overrightarrow{a}=\hat{i},\overrightarrow{b}=\hat{j},\overrightarrow{c}=\hat{k}$

$\therefore [\hat{i}+\hat{j}\hat{j}+\hat{k}\hat{k}+\hat{i}]=2\left[\hat{i}\hat{j}\hat{k}\right]=2\cdot 1=2$