A scientist is investigating the properties of a crystal. The crystal is modelled as a tetrahedron whose vertices are \(A ( 12,4 , - 1 ) , B ( 10,15 , - 3 ) , C ( 5,8,5 )\) and \(D ( 2,2 , - 6 )\), where the length of unit is the millimetre. The mass of the crystal is 0.5 grams.
Show that, to one decimal place, the area of the triangular face \(A B C\) is \(52.2 \mathrm {~mm} ^ { 2 }\)
Find the density of the crystal, giving your answer in \(\mathrm { g } \mathrm { cm } ^ { - 3 }\)