powershell, 294 bytes

Result

WA

Duration

1024ms

Code [DL]

$a =(Read-Host).Split(" ")
$b =(Read-Host).Split(" ")
$c =(Read-Host).Split(" ")
$d =(Read-Host).Split(" ")

foreach($i in 0..3){
$b[$i]-=$a$[i]
$c[$i]-=$a$[i]
$d[$i]-=$a$[i]
}
echo(($b[0]*$c[1]*$d[2]+$b[1]*$c[2]*$d[0]+$b[2]*$c[0]*$d[1]-$b[1]*$c[0]*$d[2]-$b[0]*$c[2]*$d[1]-$b[2]*$c[1]*$d[0])/6)

stdin

99 61 73
29 10 31
70 16 85
05 81 61

stdout

stderr

At line:7 char:11
+ $b[$i]-=$a$[i]
+           ~~~~
Unexpected token '$[i]' in expression or statement.
At line:8 char:11
+ $c[$i]-=$a$[i]
+           ~~~~
Unexpected token '$[i]' in expression or statement.
At line:9 char:11
+ $d[$i]-=$a$[i]
+           ~~~~
Unexpected token '$[i]' in expression or statement.
+ CategoryInfo          : ParserError: (:) [], ParentContainsErrorRecordException
+ FullyQualifiedErrorId : UnexpectedToken
 

strace