A) 1
B) 2
C) 3
D) 4
Correct Answer: D
Solution :
\[{{[\vec{a}\vec{b}\vec{c}]}^{2}}=\left| \begin{matrix} \vec{a}\cdot \vec{a} & \vec{a}\cdot \vec{b} & \vec{a}\cdot \vec{c} \\ \vec{b}\cdot \vec{a} & \vec{b}\cdot \vec{b} & \vec{b}\cdot \vec{c} \\ \vec{c}\cdot \vec{a} & \vec{c}\cdot \vec{b} & \vec{c}\cdot \vec{c} \\ \end{matrix} \right|=\left| \begin{matrix} 4 & 2 & 2 \\ 2 & 4 & 2 \\ 2 & 2 & 4 \\ \end{matrix} \right|=32\] \[[\vec{a}\,\vec{b}\,\vec{c}]=4\sqrt{2}\Rightarrow [\vec{a}\,\vec{b}\,\vec{c}]\,\cos 45{}^\circ =4\]
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