Use the triple scalar product to determine whether the given points lie in the same plane.

Question

A(1, 2, 3), B(3, -4, 8),
C(7, -1, 1), D(5, 5, -4)

Answer 1

The scalar triple product P among three vectors U,V and W is defined as follows:
P=U.(VxW)
|P| represents the volume of the parallelepiped formed by the vectors U, V and W.
Consequently, if U, V and W are coplanar, P=0.

Since 4 points (A,B,C,D) are given, three vectors can be formed where
U=AB, V=AC, and W=AD.
Calculate the triple scalar product as described above and if the result is zero, then the four points are coplanar.

Answer 2

yes