A) \[\vec{a}+(\vec{b}+\vec{c})=\vec{0}\]
B) \[\vec{a}\times (\vec{b}+\vec{c})=\vec{0}\]
C) \[\vec{a}\times (\vec{b}\times \vec{c})=\vec{0}\]
D) \[\vec{a}\,\,.\,\,(\vec{b}\times \vec{c})=\vec{0}\]
Correct Answer: C
Solution :
Now, \[\vec{a}\times (\vec{b}\times \vec{c})\] \[=(\vec{a}\,.\,\vec{b})\,\vec{c}-(\vec{a}\,.\,\vec{c})\,\vec{b}\] \[=\vec{0}-\vec{0}\] (\[\because \] \[\vec{a}\bot \vec{b}\] and \[\vec{a}\bot \vec{c}\] \[=\vec{0}\]
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