Answer
14
Work Step by Step
Step 1. Establish the three vectors for the parallelepiped: $\vec u=\vec {OP}=\langle 0,2,2 \rangle$, $\vec v=\vec {OQ}=\langle 3,1,-1 \rangle$, and $\vec w=\vec {OR }=\langle 1,4,1 \rangle$.
Step 2. Calculate the cross product $\vec u \times \vec w=\langle (2-8),(2-0),(0-2) \rangle=\langle -6,2,-2 \rangle$
(you can use other cross products, but this one is easier to calculate.)
Step 3. The volume of the parallelepiped can be found as $|\vec v\cdot (\vec u \times \vec w)|=|-18+2+2|=14$
