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Let   \vec{a},\vec{b},\vec{c},\vec{d}   are four vectors the   

\left [ \vec{a}+\vec{b}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]+ \left [ \vec{b}+\vec{c}\: \: \: \: \vec{a}\: \: \: \: \vec{d} \right ]+\left [ \vec{a}+\vec{c}\: \: \: \: \vec{b}\: \: \: \: \vec{d} \right ]    equals 

Option: 1

-1


Option: 2

0


Option: 3

1


Option: 4

2


Answers (1)

best_answer

As we have learned

Properties of Scalar Triple Product -

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

- wherein

\vec{a}, \vec{b}, \vec{c}, \vec{d} are four vectors.

 

 \left [ \vec{a}+\vec{b}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]+ \left [ \vec{b}+\vec{c}\: \: \: \: \vec{a}\: \: \: \: \vec{d} \right ]+\left [ \vec{a}+\vec{c}\: \: \: \: \vec{b}\: \: \: \: \vec{d} \right ]

= \left [ \vec{a}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]+\left [ \vec{b}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]+\left [ \vec{b}\: \: \: \: \vec{a}\: \: \: \: \vec{d} \right ]+\left [ \vec{c}\: \: \: \: \vec{a}\: \: \: \: \vec{d} \right ]+\left [ \vec{a}\: \: \: \: \vec{b}\: \: \: \: \vec{d} \right ]+\\ \left [ \vec{c}\: \: \: \: \vec{b}\: \: \: \: \vec{d} \right ]

= \left [ \vec{a}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]+\left [ \vec{b}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]+\left [ \vec{b}\: \: \: \: \vec{a}\: \: \: \: \vec{d} \right ]-\left [ \vec{a}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]-\left [ \vec{b}\: \: \: \: \vec{a}\: \: \: \: \vec{d} \right ]-\\ \left [ \vec{b}\: \: \: \: \vec{c}\: \: \: \: \vec{d} \right ]

 

 

 

 

 

 

Posted by

vishal kumar

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