Question

$\hat{i}\times (\hat{j}\times \hat{k})+\hat{j}\times (\hat{k}\times \hat{i})+\hat{k}(\hat{i}\times \hat{j})$ is equal to

• A. 1
• B. 0
• C. 3
• D. 4

Answer 1

Answer: (B)

$\hat{i}\times (\hat{j}\times \hat{k})+\hat{j}\times (\hat{k}\times \hat{i})+\hat{k}\times (\hat{i}\times \hat{j})$
$=\hat{i}\times \hat{i}+\hat{j}\times \hat{j}+\hat{k}\times \hat{k}$
$=0+0+0=0$ $[\because \hat{i}\times \hat{i}=\hat{j}\times \hat{j}=\hat{k}\times \hat{k}=0]$