Question

Let $\overline{a},\overline{b},\overline{c}$ be three non-zero vectors such that $\overline{a}+\overline{b}+\overline{c}=0,$ then $\lambda \overline{b}\times \overline{a}+\overline{b}\times \overline{c}+\overline{c}\times \overline{a}=\overline{0},$ where $\lambda$ is equal to :

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

The correct option is A $1$

$\begin{array}{c}\text{Given,}\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0\\ \Rightarrow a,b,c\text{represent that sides of a tuiangle}\\ \therefore a\times b=bxc=c\times a\\ \Rightarrow axb+bxc+c\times a=3(a\times b)\\ \Rightarrow 2b\times a+bxc+c\times a=0\\ \Rightarrow \lambda =2\\ \text{Hence, (B) is the correct option.}\end{array}$