The point equally far from four points

You will write three functions that solve the problem of the lesson in exact fractions. The checker uses the four points of the lesson.

The idea. For two points $A$ and $B$, $PA = PB$ is the linear equation $2(B - A) \cdot P = |B|^2 - |A|^2$. Three such equations, for $B$, $C$ and $D$ with the same $A$, have one solution $P$ when the four points are not in one plane. Cramer's rule solves them: each unknown is a ratio of two determinants.

Your tasks.

1. Finish det3(m). Return the determinant of a $3 \times 3$ matrix given as three rows.
2. Finish solve3(m, v). Solve $m \cdot (x, y, z) = v$ by Cramer's rule and return the three values as Fraction numbers.
3. Finish equidistant(a, b, c, d). Build the three equations and return the point that is equally far from the four points.