Planes from points

You will write three functions about planes. The first finds the plane through three points, the second tests whether a point lies on a plane, and the third finds the intercepts on the axes. A plane is stored as four numbers $(A, B, C, k)$ for $Ax + By + Cz = k$.

The idea. A normal to the plane through $P$, $Q$ and $R$ is $\overrightarrow{PQ} \times \overrightarrow{PR}$. The constant is the dot product of the normal with $P$. The plane meets the $x$-axis at $\dfrac{k}{A}$, the $y$-axis at $\dfrac{k}{B}$ and the $z$-axis at $\dfrac{k}{C}$.

Your tasks.

1. Finish plane_through(P, Q, R). Return $(A, B, C, k)$.
2. Finish on_plane(plane, point). Return True when the point satisfies the equation.
3. Finish intercepts(plane). Return the three intercepts, and give None for an intercept that does not exist.