Statement-1: Let $\vec a, \vec b, \vec c$ be three coterminous edges of a parallelopiped volume V. Let $V_1$ be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then, $V_1 =2V$.

Statement-2: For any three vectors $\vec p, \vec q,\vec r$

$\begin{bmatrix}\vec p+\vec q&\vec q+\vec r&\vec r+\vec p\end{bmatrix}=2[\vec p\,\, \vec q\,\,\vec r]$

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1.

$v=[\vec p\,\vec q\,\vec r]$

$v_1=[\vec p+\vec q,\vec q+\vec r,\vec p+\vec r]$

$=\begin{vmatrix}1&1&0\\0&1&1\\1&0&1\end{vmatrix}[\vec p\,\vec q\,\vec r]$

$v_1=2v$

so statement I, II both are correct. II is correct explanation of I.