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  • Can someone help me with this, - Vector Algebra - JEE Main-5

If \vec{a}\times \vec{b}=\vec{b}\times \vec{c}=\vec{c}\times \vec{a}  then \vec{a}+ \vec{b}+\vec{c}=

  • Option 1)

    abc

  • Option 2)

    –1

  • Option 3)

    0

  • Option 4)

    2

 

Answers (1)

best_answer

As we have learned

Properties of vector products -

\vec{a}\times \vec{b}= - (\vec{b}\times\vec{a})

- wherein

Here \vec{a} \:and\: \vec{b} are two vectors

 

 \vec{a}\times \vec{b}= \vec{b}\times \vec{c}= \vec{c}\times \vec{a}= \vec{v}

\vec{a}+\vec{b}+\vec{c} = ?

 

We have

 \vec{a}\times \vec{b} - \vec{b}\times \vec{c} = 0\\ \Rightarrow \vec{a}\times \vec{b} +\vec{b}\times \vec{c} = 0 \\ \Rightarrow (\vec{a}+\vec{c})\times \vec{b}=0 \\ similarly \: \: \: \Rightarrow (\vec{a}+\vec{b})\times \vec{c}=0 \\ and\: \: (\vec{b}+\vec{c})\times \vec{a}=0

Now \: \: (\vec{a}+\vec{c})\times \vec{b}=0 \\ \Rightarrow (\vec{a}+\vec{c})\times \vec{b} + \vec{b}\times \vec{b}= 0 \\ \Rightarrow (\vec{a}+\vec{b}+\vec{c})\times \vec{b}=0 \\(\vec{a}+\vec{b}+\vec{c})\times \vec{a}=0 \\(\vec{a}+\vec{b}+\vec{c})\times \vec{c}=0

Now (\vec{a}+\vec{b}+\vec{c})  can't be parallel to (\vec{a}\: \: \: \vec{b}\: \: \: ,\vec{c})  simuntaneously so  \vec{a}+\vec{b}+\vec{c}= 0

 

 

 

 

 

 


Option 1)

abc

Option 2)

–1

Option 3)

0

Option 4)

2

Posted by

Himanshu

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