Question

If $\hat{i},\hat{j},\hat{k}$ are the usual three perpendicular unit vectors then the value of $\hat{i}\cdot (\hat{j}\times \hat{k})+\hat{j}\cdot (\hat{i}\times \hat{k})+\hat{k}\cdot (\hat{i}\times \hat{j})$ is:

• A. $0$
• B. $-1$
• C. $3$
• D. $1$

Answer 1

The correct option is D $1$

if $\hat{i},\hat{j},\hat{k}$ are the usual three perpendicular unit vectors then 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

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

$=1-1+1$

$=1$