Question

If $\left[\begin{array}{c}\overline{a}\times \overline{b}\overline{b}\times \overline{c}\overline{c}\times \overline{a}\end{array}\right]=\lambda {\left[\begin{array}{c}\overline{a}\overline{b}\overline{c}\end{array}\right]}^2$,then $\lambda =$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is B $1$

$\begin{array}{c}\left[\overrightarrow{a}\times \overrightarrow{b}\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}\right]=\lambda {\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]}^2\\ \because \left[\overrightarrow{a}\times \overrightarrow{b}\overrightarrow{b}\times \overrightarrow{c}\overrightarrow{c}\times \overrightarrow{a}\right]={\left[abc\right]}^2\\ bycompearing\\ \therefore \lambda =1\end{array}$