Question

For non zero vectors $a,b$ and $c$, if $a+b+c=0$ then which relation true:-

• A. $a=b=c=0$
• B. $a.b=b.c=c.a$
• C. $a\times b=b\times c=c\times a$
• D. None

Answer 1

Answer: (C)

$a\times b=b\times c=c\times a$

We have,

$\begin{array}{c}a+b+c=0\\ a\times \left(a+b+c\right)=0\\ a\times a+a\times b+a\times c=0\\ a\times b=-a\times c=c\times a..............\left(1\right)\\ Similarly:\\ a\times b=b\times c\\ then,\\ a\times b=b\times c=c\times a\end{array}$

Hence, this is the answer.