If vec$(A)=2$hat$(i)-$hat$(j)+$hat$(k)$ and vec$(B)=$hat$(i)+2$hat$(j)-3$hat$(k),$ find $|(2$vec$(A)+$vec$(B))(vec(A)-2$vec$(B))|.$

Prove that $|vec(A)$vec$(B)|$ is the area of a parallelogram with sides vec$(A)$ and vec$(B).$