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  • If <img alt="\overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k} and \overrightarrow{b}=2\hat{i}+\hat{j}-3\hat{k}" src="https://learn.careers360.com/latex-image/?%5Coverrightarrow%7Ba%7D%3D%5Chat%7Bi%

If \overrightarrow{a}=\hat{i}-\hat{j}+2\hat{k} and \overrightarrow{b}=2\hat{i}+\hat{j}-3\hat{k} then \left | \overrightarrow{a}*\overrightarrow{b} \right | equals

Option: 1

\sqrt{53}

 

 

 


Option: 2

\sqrt{59}


Option: 3

\sqrt{61}


Option: 4

\sqrt{67}


Answers (1)

As we learn

Vector Product of two vectors -

\vec{a}\times \vec{b}= (a_{2}b_{3}-a_{3}b_{2})\hat{i} +(a_{3}b_{1}-a_{1}b_{3})\hat{j} +(a_{1}b_{2}-a_{2}b_{1})\hat{k}

- wherein

\vec{a}= (a_{1}\hat{i}+a_{2}\hat{j}+a_{3}\hat{k})

\vec{b}= (b_{1}\hat{i}+b_{2}\hat{j}+b_{3}\hat{k})

 

 a_{1}=1,a_{2}=-1,a_{3}=2

b_{1}=2,b_{2}=1,b_{3}=-3

\therefore \vec{a}*\vec{b}=(3-2)\hat{i}+(4+3)\hat{j}+(1+2)\hat{k}= \hat{i}+7\hat{j}+3\hat{k}

\therefore \left | \vec{a}*\vec{b} \right |=\sqrt{1+49+9}=\sqrt{59}

Posted by

Kshitij

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