Question

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

• A. $3$
• B. $2$
• C. $1$
• D. $0$

Answer 1

The correct option is C $1$

Given,

$\hat{i}\cdot (\hat{j}\times \hat{k})+\hat{j}\cdot (\hat{k}\times \hat{i})+\hat{k}\cdot (\hat{j}\times \hat{i})$
$=\hat{i}\cdot \left(\hat{i}\right)+\hat{j}\cdot \left(\hat{j}\right)+\hat{k}\cdot (-\hat{k})$
$=(\hat{i}\cdot \hat{i})+(\hat{j}\cdot \hat{j})-(\hat{k}\cdot \hat{k})$
$=1+1-1=1$