Question

If the volume of a Tetrahedron formed by coterminous edges $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ is $2$, then the volume of the parallelopiped formed by the coterminous edges $\overrightarrow{a}\times \overrightarrow{b},\overrightarrow{b}\times \overrightarrow{c},\overrightarrow{c}\times \overrightarrow{a}$ is

• A. $72$
• B. $144$
• C. $36$
• D. $108$

Answer 1

Answer: (B)

$144$

Volume of the tetrahedron $=\frac{1}{6}\left[\overline{a}\overline{b}\overline{c}\right]=2$

$\Rightarrow \left[\overline{a}\overline{b}\overline{c}\right]=12$

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

$={\left[\overline{a}\overline{b}\overline{c}\right]}^2=144$

Hence, option ${}^{\prime }B$' is correct.