import numpy as np
i = np.array([1, 0, 0])
j = np.array([0, 1, 0])
k = np.array([0, 0, 1])
(array([1, 0, 0]), array([0, 1, 0]), array([0, 0, 1]))
a = 0.7 * i + 0.5 * j + 0.50990195135 * k
b = 0.9 * i + 0.2 * j + 0.38729833462 * k
array([0.7 , 0.5 , 0.50990195])
np.sqrt(np.dot(a, a))
0.9999999999952689
np.linalg.norm(a)
0.9999999999952689
np.linalg.norm(b)
0.9999999999997128
np.arccos(np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))) / np.pi * 180
21.95402031895343
a = 0.0 * i + 1.0 * j + 0.0 * k
b = 1.0 * i + 0.0 * j + 0.0 * k
np.arccos(np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))) / np.pi * 180
90.0