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  • In general the vector <img alt="\vec{a}*(\vec{b}+\vec{c})+\vec{b}*(\vec{c}+\vec{a})+\vec{c}*\vec{b}" src="https://learn.careers360.com/latex-image/?%5Cvec%7Ba%7D*%28%5Cvec%7Bb%7D&plus;%5Cv

In general the vector \vec{a}*(\vec{b}+\vec{c})+\vec{b}*(\vec{c}+\vec{a})+\vec{c}*\vec{b} is

Option: 1

Parallel to \vec{a}

 

 


Option: 2

Parallel to \vec{c}


Option: 3

Perpendicular to both \vec{a} and \vec{c}


Option: 4

None of these 


Answers (1)

best_answer

As we learn

Properties of Vector Product -

\vec{a}\times(\vec{b}+\vec{c})= (\vec{a}\times\vec{b}) + (\vec{a}\times\vec{c})

- wherein

Vector product is distributive

 

\vec{a}*(\vec{b}+\vec{c})+\vec{b}*(\vec{c}+\vec{a})+\vec{c}*\vec{b}=\vec{a}*\vec{b}+\vec{a}*\vec{c}+\vec{b}*\vec{c}+\vec{b}*\vec{a}+\vec{c}*\vec{b}=\vec{a}*\vec{c}

hence perpenducular on both \vec{a}\ and\ \vec{c} 

Posted by

rishi.raj

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