Answer
$2\sqrt {83}$
Work Step by Step
1. Find vectors $\vec{P_1P_2}=<1,2,3>$ and $\vec{P_1P_3}=<5,4,1>$,
2. Find the cross product of the above, $\vec{P_1P_2}\times\vec{P_1P_3} =<(2*1-3*4),(3*5-1*1),(1*4-2*5)>=<-10,14,-6>$
3. Find the area of the parallelogram, $A=||\vec{P_1P_2}\times\vec{P_1P_3} ||=\sqrt {10^2+14^2+6^2}=2\sqrt {83}$
