Question

If $\overline{a}\times \overline{b}=\overline{b}\times \overline{c}=\overline{c}\times \overline{a}$ then $\overline{a}+\overline{b}+\overline{c}=?$

• A. $abc$
• B. $-1$
• C. $0$
• D. $2$

Answer 1

Answer: (C)

$0$

Let us consider $\overline{a}+\overline{b}+\overline{c}=k$

Multiply with $\overline{b}$ on both sides , we get $\overline{a}\times \overline{b}+\overline{b}\times \overline{b}+\overline{c}\times \overline{b}=k\times \overline{b}$

$\Rightarrow k\times \overline{b}=\overline{b}\times \overline{c}+0+\overline{c}\times \overline{b}=0$

Similarly we get $k\times \overline{a}=0$ and $k\times \overline{c}=0$

therefore $k=0$ for equations to satisfy

therefore correct option is $C$