Find the volume of the parallelepiped that has the vectors u⃗ as adjacent edges = <3,-3,2> and v⃗ = <3,-5,5> w⃗ = <-7,7,-8> as adjacent sides

1. Compute the cross product \(\vec{v} \times \vec{w}\):
\vec{v} \times \vec{w} = \langle 5, -11, -14 \rangle

2. Compute the dot product \(\vec{u} \cdot (\vec{v} \times \vec{w})\):
\vec{u} \cdot (\vec{v} \times \vec{w}) = 20

3. Take the absolute value of the result to obtain the volume:
V = \left| 20 \right| = 20

Answer:
V = 20