Question

If the volume of the parallelopiped with $\vec a\times \vec b$, $\vec b\times \vec c$ and $\vec c\times \vec a$ as coterminous edges is 9 cu. units,then the volume of the parallelopiped with ($\vec a\times \vec b$)×($\vec b\times \vec c$), ($\vec b\times \vec c$)×($\vec c\times \vec a$) and ($\vec c\times \vec a$)×($\vec a\times \vec b$) as coterminous edges is

• A. 9 cu.units
• B. 729 cu.units
• C. 81 cu.units
• D. 243 cu.units

Answer 1

Answer: (C)

81 cu.units

Answer 2

volume amounts to cubic units. Consequently, we can deduce that .

Now, considering the parallelepiped characterized by the edges and , its volume is given by the expression , and its numerical value is presented as:

Hence, the overall volume of this parallelepiped equates to 81 cubic units.

The correct answer is option (C): 81 cu.units