A) \[a.\,b=b.\,c=c.\,b=0\]
B) \[a\times b=b\times c=c\times a\]
C) \[a.\,b=b.\,c=c.\,a=0\]
D) \[a\times a+a\times c+c\times a=0\]
Correct Answer: B
Solution :
If a, b and c are the sides of a triangle, then a + b + c = 0. Since, \[a+b+c=0\] \[\Rightarrow \] \[a+b=-c\] \[\Rightarrow \] \[(a+b)\times c=-c\times c\] \[\Rightarrow \] \[a\times c+b\times c=0\] \[\Rightarrow \] \[b\times c=c\times a\] Similarly, \[a\times b=b\times c\] Hence, \[a\times b=b\times c=c\times a\]
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