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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%7Bc%7D

Let \overrightarrow{a},\overrightarrow{b},\overrightarrow{c} are three non-zero vectors then \left | \overrightarrow{a}*\overrightarrow{b}+\overrightarrow{b}*\overrightarrow{c}+\overrightarrow{c}*\overrightarrow{a}+\overrightarrow{b}*\overrightarrow{a}+\overrightarrow{c}*\overrightarrow{b}+\overrightarrow{a}*\overrightarrow{c}\right | equals 

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

3


Answers (1)

best_answer

As we learn

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{b}*\vec{a}= -(\vec{a}*\vec{b})\Rightarrow \vec{a}*\vec{b}+\vec{b}*\vec{a}=\vec{0}

\therefore \vec{b}*\vec{c}= -(\vec{c}*\vec{b})\Rightarrow \vec{b}*\vec{c}+\vec{c}*\vec{b}=\vec{0}

\therefore \vec{c}*\vec{a}= -(\vec{a}*\vec{c})\Rightarrow \vec{c}*\vec{a}+\vec{a}*\vec{c}=\vec{0}

\therefore \vec{a}*\vec{b}+\vec{b}*\vec{c}+\vec{c}*\vec{a}+\vec{b}*\vec{a}+\vec{c}*\vec{b}+\vec{a}*\vec{c}=\vec{0}

\therefore it's magnitude =zero

 

Posted by

Ritika Jonwal

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