Answer
$16$
Work Step by Step
$P(3,0,1),Q(-1,2,5), R(5,1,-1)$ and $S(0,4,2)$
$a=PQ ^\to=\lt -1-3,2-0,5-1\gt=\lt -4,2,4 \gt$
$b=PR ^\to=\lt 5-3, 1-0, -1-1\gt=\lt 2,1,-2 \gt$
$c=PS ^\to=\lt 0-3, 4-0, 2-1\gt=\lt -3,4,1 \gt$
Volume of a parallelepiped is defined as:
$V=|a \cdot (b \times c)|$
$b \times c=\lt 2,1,-2 \gt \times \lt -3,4,1 \gt=\lt 9,4,11 \gt$
$|a \cdot (b \times c)|= |\lt -4,2,4 \gt \cdot \lt 9,4,11 \gt|$
$=|-4 \cdot 9+2 \cdot 4+ 4 \cdot 11|$
$=16$
