Let the vectors → a , → b , → c represent three coterminous edges...

We know that,

Volume of parallelepiped whose edges determined by vectors $\overset{\to}{a}, \overset{\to}{b}, \overset{\to}{c}$ is \left[$\begin{cases}\overset{\to}{a} & \overset{\to}{b} & \overset{\to}{c}\end{cases}$\right]$.</p><p>Now it is given that$V$is volume of parallelepiped$\overset{\to}{a}, \overset{\to}{b}, \overset{\to}{c}$, so required volume of parallelepiped with new edges will be</p><p>$= \left[$\begin{cases}\overset{\to}{a} & \overset{\to}{b} + \overset{\to}{c} & \overset{\to}{a} + 2\overset{\to}{b} + 3\overset{\to}{c}\end{cases}$\right]$</p><p>$= \left|$\begin{cases}1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 2 & 3\end{cases}$\right|\left[$\begin{cases}\overset{\to}{a} & \overset{\to}{b} & \overset{\to}{c}\end{cases}$\right]$</p><p>$= \left\{\left(1\right)\left(3 - 2\right) - 0 + 0\right\}\left[$\begin{cases}\overset{\to}{a} & \overset{\to}{b} & \overset{\to}{c}\end{cases}$\right]$</p><p>$= \left[$\begin{cases}\overset{\to}{a} & \overset{\to}{b} & \overset{\to}{c}\end{cases}$\right]$</p><p>$= V

Hence this is the correct option.