The angle between two lines by computer

You will write functions for the dot product of two direction vectors, the acute angle between two lines and a test that says whether two lines are perpendicular, parallel or neither. The cross product is already written for you.

The idea. The acute angle has $\cos\theta = \dfrac{\lvert \vec{u} \cdot \vec{v} \rvert}{\lvert \vec{u} \rvert \lvert \vec{v} \rvert}$. Lines are perpendicular when the dot product is $0$, and parallel when the cross product is the zero vector.

Your tasks.

1. Finish dot(u, v). Add the three products of matching components.
2. Finish angle_between(u, v). Return the acute angle in degrees.
3. Finish relation(u, v). Return "perpendicular", "parallel" or "neither".