Question

If $(a\times b)\cdot (b\times c)\times (c\times a)=[a\cdot (b\times c){]}^k$, then the value of $k$ is equal to

• A. 4
• B. 2
• C. 1
• D. 0

Answer 1

The correct option is B 2

$(\overline{a}\times \overline{b})\cdot \left\{\right(\overline{b}\times \overline{c})\times (\overline{c}\times \overline{a}\left)\right\}$
$=(\overline{a}\times \overline{b})\cdot \{\left[\overline{b}\overline{c}\overline{a}\right]\overline{c}-\left[\overline{b}\overline{c}\overline{c}\right]\overline{a}\}=(\overline{a}\times \overline{b})\cdot \overline{c}\left(\left[\overline{b}\overline{c}\overline{a}\right]\right)={\left[\overline{a}\overline{b}\overline{c}\right]}^2$