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MCQ

$\frac{{\left[ {\left( {\vec a \times \vec b} \right) \times \left( {\vec b \times \vec c} \right)\left( {\vec b \times \vec c} \right) \times \left( {\vec c \times \vec a} \right)\left( {\vec c \times \vec a} \right) \times \left( {\vec a \times \vec b} \right)} \right]}}{{\left[ {\vec a \times \vec b\,\,\,\,\vec b \times \vec c\,\,\,\,\vec c \times \vec a} \right]}}$ is equal to

A
${\left| {\vec a} \right|^2}\,{\left| {\vec b} \right|^2}\,{\left| {\vec c} \right|^2}$
✓
${\left[ {\vec a\,\,\vec b\,\,\vec c} \right]^2}$
C
$\frac{{\left[ {\vec a \times \vec b\,\,\vec b \times \vec c\,\,\vec c \times \vec a} \right]}}{2}$
D
$\frac{{{{\left| {\vec a} \right|}^2}\,{{\left| {\vec b} \right|}^2}\,{{\left| {\vec c} \right|}^2}}}{2}$

✓

Answer

Correct option: B.

${\left[ {\vec a\,\,\vec b\,\,\vec c} \right]^2}$

b

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