Dot products and angles by computer

You will write three functions for vectors given as tuples: the dot product, the angle between two vectors in degrees, and a test for perpendicular vectors. The checker uses vectors of the lesson, including a pair that point in opposite directions.

The idea. The dot product adds the products of the matching components. The angle is the inverse cosine of the dot product divided by both magnitudes. Two vectors are perpendicular when the dot product is zero. A computer keeps a few decimal places only, so the test compares with a very small number.

Your tasks.

1. Finish dot(a, b). Add the products of the matching components.
2. Finish angle_between(a, b). Return the angle in degrees. Use acos and degrees.
3. Finish is_perpendicular(a, b). Return True when the dot product is within $10^{-9}$ of zero.