The three concurrent edges of a parallelopiped represent the vectors $\vec a,\vec b,\vec c$ such that $[\vec a\,\,\vec b\,\,\vec c]=V$. Then, the volume of the parallelopiped whose three concurrent edges are the three diagonals of three faces of the given parallelopiped is

2 V

The volume of the parallelopiped having concurrent edges as the diagonals of three faces of the given parallelopiped is given by

$\begin{bmatrix}\vec a+\vec b&\vec b+\vec c&\vec c+\vec a\end{bmatrix}=2[\vec a\,\,\vec b\,\,\vec c]=2V$