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If \vec{a} and \vec{b} are non-zero vectors, such that \vec{a}* \vec{b}=\vec{b}*\vec{a} then

Option: 1

\left | \vec{a} \right |=0

 

 

 


Option: 2

\left | \vec{b} \right |=0


Option: 3

\left | \vec{a} \right |=\left | \vec{b} \right |


Option: 4

\vec{a} and \vec{b} are collinear


Answers (1)

best_answer

As we learn

Properties of Vector Product -

\vec{a}\times\vec{b}\neq \vec{b}\times\vec{a}

- wherein

Vector Product is not Commutative

 

 \vec{a}*\vec{b} is not always equal to \vec{b}*\vec{a} , instead \vec{a}*\vec{b}=-\vec{b}*\vec{a}

 

\therefore \vec{a}*\vec{b}=-\vec{b}*\vec{a} becomes \therefore 2(\vec{a}*\vec{b})=\vec{0}\Rightarrow -\vec{a}*\vec{b}=\vec{0}

\Rightarrow sin\Theta =0 (\therefore \left | \vec{a} \right |\neq 0,\left | \vec{b}\ \right |\neq 0)

\therefore \vec{a} and \vec{b} are collinear

Posted by

Shailly goel

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