A) \[a=b=c=0\]
B) any two of\[a,\,\,b\]and\[c\]are zero
C) any one of\[a,\,\,b\]and\[c\]is zero
D) \[a+b+c=0\]
Correct Answer: B
Solution :
We have,\[|a\mathbf{\hat{i}}+b\mathbf{\hat{j}}+c\mathbf{\hat{k}}|=|a|+|b|+|c|\] \[\Rightarrow \]\[\sqrt{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}}=|a|+|b|+|c|\] \[\Rightarrow \]\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] \[={{a}^{2}}+{{b}^{2}}+{{c}^{2}}(|a||b||+|b||c|+|c||a|)\] \[\Rightarrow \]\[|a||b|+|b||c|+|c||a|\,\,=0\] \[\Rightarrow \]\[ab=bc=ca=0\] \[\Rightarrow \]Any two of\[a,\,\,b\]and\[c\]are zero.
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