Volumes and coplanar points by computer

You will write three functions: the scalar triple product of three vectors, the volume of a tetrahedron from its four corners and a test for four points in one plane. The checker uses the numbers of the lesson.

The idea. The triple product is the determinant of the three vectors. The tetrahedron has one sixth of the volume of the parallelepiped on three edges from one corner. Four points are coplanar when the triple product of the three edges from one of them is zero.

Your tasks.

1. Finish triple(a, b, c). Compute $\vec a\cdot(\vec b\times\vec c)$.
2. Finish tetra_volume(A, B, C, D). Use the edges from A.
3. Finish coplanar(A, B, C, D). Return True when the triple product is zero.