A small vector toolkit

You will write three functions for a vector given as a tuple of three numbers: its magnitude, its unit vector and its direction angles. The checker tests them on several vectors, including ones with negative components.

The idea. The magnitude is the square root of the sum of the squares of the components. The unit vector divides every component by the magnitude. The angle with an axis is the inverse cosine of the matching direction cosine.

Your tasks.

1. Finish magnitude(v). Return $\sqrt{x^2 + y^2 + z^2}$.
2. Finish unit_vector(v). Return a tuple of three numbers.
3. Finish direction_angles(v). Return the three angles in degrees, as a tuple.