Calculates the area of a parallelogram given the coordinates (x,y,z) of three points.

import numpy as np

def get_vector(name):
    while True:
        raw = input("Enter vector " + name + " as three \n comma-separated numbers \n(e.g., 1, 2, 3): ")
        try:
            parts = [float(x.strip()) for x in raw.split(",")]
            if len(parts) != 3:
                print("Please enter exactly three values.")
                continue
            return parts
        except ValueError:
            print("Invalid input. Make sure all entries are numbers.")

print("Before we begin, remember:\n q must lie between p and r \n along the same line.\n")

p = get_vector("p")
q = get_vector("q")
r = get_vector("r")

def a(p, q, r):
    PQ = np.array(q) - np.array(p)
    PR = np.array(r) - np.array(p)
    cross_product = np.cross(PQ, PR)
    area = np.sqrt(np.sum(cross_product**2))
    return area

area = a(p, q, r)
print("\nThe area of the parallelogram \n formed by PQ and PR is: \n" + str(round(area,3)))