Question

The value of $\hat{i}.(\hat{j}\times \hat{k})+\hat{j}.(\hat{i}\times \hat{k})+\hat{k}.(\hat{i}\times \hat{j})$ is :

• A. $0$
• B. $-1$
• C. $1$
• D. None of these

Answer 1

The correct option is C $1$

We know,

$\hat{j}\times \hat{k}=\hat{i},\hat{i}\times \hat{k}=-\hat{j},\hat{i}\times \hat{j}=\hat{k}$

Therefore,

$\hat{i}.(\hat{j}\times \hat{k})+\hat{j}.(\hat{i}\times \hat{k})+\hat{k}.(\hat{i}\times \hat{j})$

$=\hat{i}.\hat{i}+\hat{j}.(-\hat{j})+\hat{k}.\hat{k}$

$=1-1+1=1$