Question

If $\hat{i}\times \hat{j}+\hat{i}\times \hat{k}+\hat{j}\times \hat{k}+\hat{k}\times \hat{i}=x\hat{i}+y\hat{j}+z\hat{k},$ then the value of $x+y+z=$

• A. $2$
• B. $3$
• C. $-1$
• D. $0$

Answer 1

The correct option is A $2$

Given : $\hat{i}\times \hat{j}+\hat{i}\times \hat{k}+\hat{j}\times \hat{k}+\hat{k}\times \hat{i}=x\hat{i}+y\hat{j}+z\hat{k}$
$\Rightarrow x\hat{i}+y\hat{j}+z\hat{k}=\hat{k}-\hat{j}+\hat{i}+\hat{j}=\hat{i}+\hat{k}$
$\therefore x=1,y=0$ and $z=1$