ruby, 105 bytes

Result

AC

Duration

549ms

Code [DL]

require'matrix'
a,b,c,d=STDIN.read.lines.map{|l|Vector[*l.split.map(&:to_i)]}
p Matrix[b-a,c-a,d-a].det/6

stdin

14 47 97
20 36 74
83 07 69
14 09 67

stdout

6392

stderr

strace