A) \[\vec{a}\times \vec{b}\]
B) \[\vec{c}\times \vec{b}\,\]
C) \[\vec{a}\times \vec{c}\]
D) None of these
Correct Answer: A
Solution :
| [a] \[\vec{a}\,+\vec{b}\,+\vec{c}=0\] |
| \[\therefore \] \[\vec{a}\,+\vec{c}=-\vec{b}\] |
| \[\therefore \] \[(\vec{a}\,+\vec{c})\,\times \,\vec{b}\,=-\vec{b}\,\times \,\vec{b}=0\] |
| or \[(\vec{a}\,\times \,\vec{b})\,+\,(\vec{c}\times \,\vec{b})=0\] |
| or \[\vec{a}\times \,\vec{b}\,=\vec{b}\times \,\vec{c}\] |
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