Question

If $[\overrightarrow{a}\times \overrightarrow{b}\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}]=\lambda [\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}{]}^2$, then $\lambda$ is equal to

• A. $2$
• B. $3$
• C. $0$
• D. $1$

Answer 1

The correct option is D $1$

$\begin{array}{c}\left[\overrightarrow{a}\times \overrightarrow{b}\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}\right]=\left(\overrightarrow{a}\times \overrightarrow{b}\right)\cdot \left[\left(\overrightarrow{b}\times \overrightarrow{c}\right)\times \left(\overrightarrow{c}\times \overrightarrow{a}\right)\right]\\ =\left(\overrightarrow{a}\times \overrightarrow{b}\right)\cdot \left(\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]\overrightarrow{c}\right)\\ Implie\lambda =1\\ Hence,thecorrectoptionis\left(D\right)\end{array}$