Find the volume of parallelepiped (in m³) whose edges are represented by $a=(2\widehat{i}-3\widehat{j}+4\widehat{k})m,b=(\widehat{i}+2\widehat{j}-\widehat{k})m$ $\text{ and }c=(3\widehat{i}-\widehat{j}+2\widehat{k})m\text{. }$

$\text{ The volume of parallelepiped is }|\overrightarrow{a}\cdot (\overrightarrow{b}\times \overrightarrow{c}\left)\right|$

$\begin{array}{l}=\left|\right(2\tilde{i}-3\tilde{j}+4\tilde{k})\cdot \{(\tilde{i}+2\tilde{j}-\tilde{k})\times 3\tilde{i}-\tilde{j}+2\tilde{k}\left\}\right|\\ =\left|(2\widehat{i}-3\widehat{j}+4\widehat{k})\cdot \left\{\begin{array}{ccc}\widehat{i}& \widehat{j}& \widehat{k}\\ 1& 2& -1\\ 3& -1& 2\end{array}\mid \right\}\right|\\ =(2\tilde{i}-3\tilde{j}+4\tilde{k})\cdot \left\{\right(4-1)-\tilde{j}(2+3)+\tilde{k}(-1-6\left)\right\}\mid \\ =\left|\right(2\widehat{i}-3\widehat{j}+4\widehat{k})\cdot (3\widehat{i}-5\widehat{j}-7\widehat{k}\left)\right|\\ =|6+15-28|=7m^3\end{array}$