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Let \vec{a},\vec{b},\vec{c},\vec{d}, are four vectors then \begin{bmatrix} \vec{a}+\vec{b} &\vec{c} &\vec{d} \end{bmatrix}+\begin{bmatrix} \vec{c} &\vec{a} &\vec{d} \end{bmatrix}+\begin{bmatrix} \vec{d} &\vec{c} &\vec{b} \end{bmatrix} equals

Option: 1

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Option: 2

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Option: 3

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Answers (1)

best_answer

As we learn

Properties of Scalar Triple Product -

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

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

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

\therefore \left [ \vec{a}+\vec{b}\ \vec{c}\ \vec{d}\right ]+\left [ \vec{c}\vec{a}\vec{d} \right ]+\left [ \vec{d}\vec{c}\vec{b} \right ]=0

 

Posted by

Ritika Kankaria

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