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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)\; equals" src="https://learn.careers360.com/latex-image/?%5Chat%20%7Bi%7D%20%5Ctimes%2

\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 0


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{i}\times \hat{j}+\hat{i}\times \hat{k}+\hat{j}\times \hat{k}+\hat{j}\times \hat{ i}+\hat{k}\times \hat{i}+\hat{k}\times \hat{j}

= \hat{k}- \hat{j}+\hat{i}-\hat{k}+\hat{j}-\hat{i}= \vec{0}

 

Posted by

Sanket Gandhi

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