Question

Calculate the volume of the tetrahedron whose vertices are the points A = (3, 2, 1),
B = (1, 2, 4), C = (4, 0, 3) and D = (1, 1, 7).

Answer 1

a = 3i+2j+k
b = i+2j+4k
c = 4i+3k
d = i+j+7k
AB = b-a = -2i+3k
AC = c-a = i-2j+2k
AD = d-a = -2i-j+6k
volume =1/6[AB AC AD] = 1/6 det(AB AC AD)
             =  1/6(5)
              = 5/6 units³