### Instruction: Let $\theta$ be the angle between the planes $2x + y - 2z + 3 = 0$ and $6x + 3y + 2z - 5 = 0.$  Find $\cos \theta.$ Let's write a Python program to solve it.### Response: import numpy as np

# define the normal vectors to the planes
n1 = np.array([2, 1, -2])
n2 = np.array([6, 3, 2])

# compute the dot product of n1 and n2
dot_product = np.dot(n1, n2)

# compute the magnitudes of n1 and n2
n1_magnitude = np.linalg.norm(n1)
n2_magnitude = np.linalg.norm(n2)

# compute the cosine of the angle between the planes
cos_theta = dot_product / (n1_magnitude * n2_magnitude)

print(cos_theta)