A) \[b\bot \,\,c\]
B) \[a\bot \,\,b\]
C) \[a||\,\,c\]
D) \[a\bot \,c\]
Correct Answer: C
Solution :
Given, a, b and c are non-zero. vectors and \[a.\,\,(b\times c)=0\] If \[a||c\,\,\Rightarrow \,\,a=\lambda c,\] where \['\lambda '\] is arbitrary constant. Then, \[[a\,\,\,b\,\,\,\,c]\,\,=\,[\lambda c\,\,\,\,b\,\,\,\,c]\] \[=\lambda [c\,\,\,\,b\,\,\,\,c]=\lambda .0=0\] (\[\because \] two vectors are same)
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