\[\text {volume of }B' = \answer {20}\,\text {cubic units}\]
Let \(B\) be a parallelepiped determined by vectors \(\vec {u}\), \(\vec {v}\), and \(\vec {w}\) in \(\RR ^3\). Suppose the volume
of \(B\) is 10 cubic units. Let \(B'\) be a parallelepiped determined by \(-\vec {u}\), \(2\vec {v}\), and \(\vec {w}+\vec {u}\). Find the volume
of \(B'\).