Bisectors, bisecting points and volumes

You will write three functions. The first finds the plane that is equally far from two points. The second finds the volume of a tetrahedron. The third decides which bisecting plane of two planes bisects the obtuse angle. A plane is stored as $(A, B, C, k)$ for $Ax + By + Cz = k$.

The idea. The plane equidistant from $A$ and $B$ has normal $B - A$ and passes through the midpoint. The tetrahedron has volume $\dfrac{1}{6}\lvert \overrightarrow{AB} \cdot (\overrightarrow{AC} \times \overrightarrow{AD}) \rvert$. For two planes $A_1x + B_1y + C_1z + D_1 = 0$ with $D_1 > 0$ and $D_2 > 0$, the plus bisector bisects the obtuse angle when $\vec{n}_1 \cdot \vec{n}_2 > 0$.

Your tasks.

1. Finish bisector_of_points(A, B). Return $(a, b, c, k)$ with $(a, b, c) = B - A$.
2. Finish tetra_volume(A, B, C, D).
3. Finish obtuse_sign(plane1, plane2). The planes are $(A, B, C, D)$ for $Ax + By + Cz + D = 0$. Change the sign of a plane with a negative $D$ first. Return "+" when the plus bisector is the obtuse one and "-" otherwise.