Question

Value of $(a\times b)\cdot ((b\times c)\times (c\times a))$ is

• A. $\left[abc\right]$
• B. ${\left[abc\right]}^2$
• C. ${\left[abc\right]}^3$
• D. None of thees

Answer 1

The correct option is B ${\left[abc\right]}^2$

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