A) \[\vec{a}+\vec{b}+\vec{c}=0\]
B) \[\vec{a},\vec{b},\vec{c}\]are mutually perpendicular
C) \[\vec{a},\vec{b},\vec{c}\]are parallel
D) \[\vec{a},\vec{b},\vec{c}\]can be any three arbitrary vectors
E) \[\vec{a},\vec{b},\vec{c}\]are coplanar vectors
Correct Answer: D
Solution :
For any three arbitrary vectors\[\overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c}\] \[\overrightarrow{a}\times (\vec{b}\times \overrightarrow{c})+\overrightarrow{b}\times (\overrightarrow{c}\times \overrightarrow{a})+\overrightarrow{c}(\overrightarrow{a}\times \overrightarrow{b})=\overrightarrow{0}\] (Always true).
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