To find a normal to a plane， We need

  1. at least three points on the plane, or
  2. two vectors

Here are the steps:

  1. if you have three points p1, p2, p3, you need to obtain two vectors from these points
  2. find the corss product from these two vectors

Explain using code

import numpy as np

# numpy is a python package that allows you do matrix operation
# we can use array([x, y, z]) to define some points
p1 = np.array([0,0,1])
p2 = np.array([2,2,3])
p3 = np.array([0,3,1])

# by subtracting point from another point, we can calculate
# the vector in the plane
v1 = p2 - p1
v2 = p3 - p1

# Now, if we take the cross product of v1 and v2, we get a
# vector v3 that is normal to these two vector, and that is
# the vector normal to the plane of v1 and v2.

v3 = np.cross(v1, v2)
print(v3)