A) \[m<0\]
B) \[m>0\]
C) \[m=0\]
D) \[m=3\]
Correct Answer: A
Solution :
We have, \[a+b+c=0\] \[\Rightarrow \]\[{{\left| a+b+c \right|}^{2}}=0\] \[\Rightarrow \]\[{{\left| \,a\, \right|}^{2}}+{{\left| \,b\, \right|}^{2}}+{{\left| \,c\, \right|}^{2}}\] \[+2\{a\cdot b+b\cdot c+c\cdot a\}=0\] \[\Rightarrow \]\[a\cdot b+b\cdot c+c\cdot a\] \[=-\frac{1}{2}\{{{\left| \,a\, \right|}^{2}}+{{\left| \,b\, \right|}^{2}}+{{\left| \,c\, \right|}^{2}}\}<0\] \[\Rightarrow \] \[m<0\]
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