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Let  \vec{a},\vec{b},\vec{c} are three non-coplanar vectors , and \vec{a^{'}},\vec{b^{'}},\vec{c^{'}} are reciprocal system of vectors then \vec{a}\cdot\vec{a}^{'}'+\vec{b}\cdot\vec{b^{'}}+\vec{c}\cdot\vec{c^{'}} equals 

Option: 1

1


Option: 2

2


Option: 3

3


Option: 4

4


Answers (1)

best_answer

As we have learned

Reciprocal System of Vectors -

\vec{a}\cdot \vec{a'}=\vec{b}\cdot \vec{b'}=\vec{c}\cdot \vec{c'}=1

- wherein

\vec{a}, \vec{b}, \vec{c}are vectors 

\vec{a} \ {}', \vec{b} \ {}', \vec{c} \ {}'are reciprocal system of vectors.

 

 \because \vec{a}\cdot\vec{a^{'}}=\vec{b}\cdot\vec{b^{'}}=\vec{c}\cdot\vec{c^{'}}=1

\therefore \vec{a}\cdot\vec{a^{'}}+\vec{b}\cdot\vec{b^{'}}+\vec{c}\cdot\vec{c^{'}}=3

             

 

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Rakesh

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