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  • <img alt="\hat{i}\times (\hat{j}+\hat{k})+\hat{j}\times (\hat{k}+\hat{i})+\hat{k}\times (\hat{i}+\hat{j})" src="https://learn.careers360.com/latex-image/?%5Chat%7Bi%7D%5Ctimes%20%28%5Chat%7Bj%7D&am

\hat{i}\times (\hat{j}+\hat{k})+\hat{j}\times (\hat{k}+\hat{i})+\hat{k}\times (\hat{i}+\hat{j}) equals

 

Option: 1

3\hat{i}

 

 

 


Option: 2

3\hat{j}


Option: 3

3\hat{k}


Option: 4

\vec{O}


Answers (1)

best_answer

As we have learned

Vector Product of Unit Vectors -

\vec{i}\times \vec{j}=\vec{k}

\vec{j}\times \vec{k}=\vec{i}

\vec{k}\times \vec{i}=\vec{j}

- wherein

\vec{i},\vec{j},\vec{k} are unit vectors

 

 \hat i \times (\hat j + \hat k ) + \hat j \times (\hat k + \hat i ) + \hat k \times (\hat i + \hat j )

= \hat k - \hat j + \hat i -\hat k +\hat j -\hat i

= \vec 0

 

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