A) \[(\mathbf{a}+\mathbf{c})\,\bot \,\mathbf{b}\]
B) \[(\mathbf{a}+\mathbf{c})\,\,|\,\,|\,\,\mathbf{b}\]
C) \[\mathbf{a}+\mathbf{c}=\mathbf{b}\]
D) None of these
Correct Answer: B
Solution :
\[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{c}\Rightarrow (\mathbf{a}+\mathbf{c})\,\times \,\,\mathbf{b}=0,\]but \[\mathbf{a}+\mathbf{c}\ne 0\] \[\Rightarrow \mathbf{a}+\mathbf{c}||\mathbf{b}.\]
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