If \([\bar{a} \bar{b} \bar{c}]=3\), then the volume of the parallelopiped with \(2 \bar{a}+\bar{b}, 2 \bar{b}+\bar{c}, 2 \bar{c}+\bar{a}\) as coterminus edges is

Volume of parallelepiped
\(=(2 \bar{a}+\bar{b}) \cdot[(2 \bar{b}+\bar{c}) \times(2 \bar{c}+\bar{a})] \)
\( =(2 \bar{a}+\bar{b}) \cdot[(4 \bar{b} \times \bar{c})+(2 \bar{b} \times \bar{a})+(2 \bar{c} \times \bar{c})+(\bar{c} \times \bar{a})] \)
\( =[8 \bar{a} \cdot(\bar{b} \times \bar{c})]+[4 \bar{a} \cdot(\bar{b} \times \bar{a})]+[2 \bar{a} \cdot(\bar{c} \times \bar{a})]+\) \([4 \bar{b} \cdot(\bar{b} \times \bar{c})]+[2 \bar{b} \cdot(\bar{b} \times \bar{a})]+[\bar{b} \cdot(\bar{c} \times \bar{a})] \)
\( =[8 \bar{a} \cdot(\bar{b} \times \bar{c})]+0+[\bar{b} \cdot(\bar{c} \times \bar{a})] \)
\( =8[\bar{a} \cdot(\bar{b} \times \bar{c})]+[\bar{a} \cdot(\bar{b} \times \bar{c})]=9 \bar{a} \cdot(\bar{b} \times \bar{c}) \)
\( =9[\bar{a} \quad \bar{b} \quad \bar{c}]=9(3)=27\)