Question

Let $a,b,c$ be three non-zero vectors such that $a+b+c=0$, then $\lambda b\times a+b\times c+c\times a=0$, where $\lambda$ is

• A. $1$
• B. $2$
• C. $-1$
• D. $-2$

Answer 1

The correct option is B $2$

Clearly $a,b,c$ represents the sides of a triangle.
Therefore, $a\times b=b\times c=c\times a$
$\Rightarrow a\times b+b\times c+c\times a=3a\times b$
$\Rightarrow 2b\times a+b\times c+c\times a=0$
$\Rightarrow \lambda =2$