Cross products and areas by computer

You will write three functions for vectors given as tuples of three numbers: the cross product, the area of a triangle from its three corners, and a test for parallel vectors. The checker uses the vectors of the lessons.

The idea. The components of the cross product come from the determinant. The triangle has half the size of the cross product of two sides from one corner. Two vectors are parallel when their cross product is the zero vector.

Your tasks.

1. Finish cross(a, b). Return a tuple of three numbers.
2. Finish triangle_area(P, Q, R). Use the sides from P, and the function cross.
3. Finish is_parallel(a, b). Return True when every component of the cross product is zero.