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  • Let <img alt="\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}" src="https://learn.careers360.com/latex-image/?%5Coverrightarrow%7Ba%7D%2C%5Coverrightarrow%7Bb%7D%2C%5Coverrightarrow%7

Let \overrightarrow{a},\overrightarrow{b},\overrightarrow{c} are three non-zero vectors then \overrightarrow{a}*(\overrightarrow{b}+\overrightarrow{c}) +\overrightarrow{b}*(\overrightarrow{c}+\overrightarrow{a})+\overrightarrow{c}*(\overrightarrow{a}+\overrightarrow{b}) equals

Option: 1

2\overrightarrow{a}


Option: 2

2\overrightarrow{b}


Option: 3

2\overrightarrow{c}


Option: 4

\overrightarrow{0}


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

Here \vec{a}, \vec{b}\: and\: \vec{c} are three vectors

 

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

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

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

\vec{0}+\vec{0}+\vec{0}=\vec{0}

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Sayak

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