Mixed product

Let u, v and w vectors. We define the mixed product (triple or box product, too) of u, v and w as the number:

Exercise: Let the points A(1,1,1),B(1,3,0),C(2,-1,2),D(1,0,-3). Calculate:
a) (AB,AC,AD)
b) The volume of the parallelepiped defined by AB, AC and AD
c) The volume of the tetrahedron ABCD
Solutions: a) 9; b) 9u3; c) 3/2u3

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