## Calculus: Early Transcendentals 8th Edition

$16$
$P(-2,1,0),Q(2,3,2), R(1,4,-1)$ and $S(3,6,1)$ $a=PQ ^\to=\lt 2+2,3-1,2-0\gt=\lt 4,2,2 \gt$ $b=PR ^\to=\lt 1+2, 4-1, -1-0\gt=\lt 3,3,-1 \gt$ $c=PS ^\to=\lt 3+2, 6-1, 1-0\gt=\lt 5,5,1 \gt$ Volume of a parallelepiped is defined as: $V=|a \cdot (b \times c)|$ $b \times c=\lt 3,3,-1 \gt \times \lt 5,5,1 \gt=\lt 8,-8,0 \gt$ $|a \cdot (b \times c)|= |\lt 4,2,2 \gt \cdot \lt 8,-8,0 \gt|$ $=|4 \cdot 8+2 \cdot -8+ 2 \cdot 0|$ $=|16|$ $=16$