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  • Let   are three non coplanar vector , then <img alt="\v

Let \vec a ,\vec b, \vec c  are three non coplanar vector , then \vec a \times \vec a + \vec b \times \vec b + \vec c \times \vec c  equals 

Option: 1

\vec a


Option: 2

\vec 0


Option: 3

\vec b


Option: 4

\vec c


Answers (1)

best_answer

As we have learned

Reciprocal System of Vectors. -

\vec{a} \ {}\cdot \vec{b} \ {}'=\vec{a} \ \cdot \vec{c} \ {}' = \vec{b}\cdot \vec{a} \ {}' \\= \vec{b} \ \vec{c}\ {}' = \vec{c} \ \vec{b}\ {}' = \vec{c}. \ \vec{a}\ {}' =0

- wherein

\vec{a}, \vec{b}, \vec{c}are vectors 

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

 

 \vec{a}\times \vec{a}+\vec{b}\times \vec{b}+\vec{c}\times \vec{c}=\frac{\vec{a}\times (\vec{b}\times \vec{c})+\vec{b}\times (\vec{c}\times \vec{a})+\vec{c}\times (\vec{a}\times \vec{b})}{\left [ \vec{a}\; \; \vec{b}\: \: \vec{c}\right ]}

= \vec 0

 

Posted by

seema garhwal

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