Skew, parallel or intersecting

You will write three functions that work on two lines in space. They find the scalar triple product, sort the lines into three kinds and find the shortest distance between them. The functions for the dot and cross product are given.

The idea. A line is a point $\vec{a}$ and a direction $\vec{b}$. The lines are parallel when $\vec{b}_1 \times \vec{b}_2 = \vec{0}$. Otherwise they intersect when $(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2) = 0$, and they are skew when it is not zero.

Your tasks.

1. Finish triple(a1, b1, a2, b2). Return $(\vec{a}_2 - \vec{a}_1) \cdot (\vec{b}_1 \times \vec{b}_2)$.
2. Finish kind(a1, b1, a2, b2). Return "parallel", "intersecting" or "skew".
3. Finish distance(a1, b1, a2, b2). Use the skew formula, or the parallel formula when the lines are parallel.