Question

If $\left[\begin{array}{ccc}\overline{a}& \overrightarrow{b}& \overrightarrow{c}\end{array}\right]=4$ then $\left[\begin{array}{cccc}\overrightarrow{a}& \times \overrightarrow{b}& b\times \overrightarrow{c}& \overrightarrow{c}\times \overrightarrow{a}\end{array}\right]=$

• A. 4
• B. 2
• C. 8
• D. 16

Answer 1

The correct option is D 16

$\left[\overline{a}\overline{b}\overline{c}\right]=4$

$[\overline{a}\times \overline{b}$ $\overline{b}\times \overline{c}$ $\overline{c}\times \overline{a}]$

$=(\overline{a}\times \overline{b}).\left[\right(\overline{b}\times \overline{c})\times (\overline{c}\times \overline{a}\left)\right]$

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

$=(\overline{a}\times \overline{b}).\left[\overline{c}\right[bca]-\overline{a}\times \overline{0}]$

$=(\overline{a}\times \overline{b}).\overline{c}\left[\overline{b}\overline{c}\overline{a}\right]$

$=\left[\overline{a}\overline{b}\overline{c}\right]\left[\overline{a}\overline{b}\overline{c}\right]$

$=[abc{]}^2$

$=4^2=16$