import numpy as np

# Vocabulary and lookup
vocab = ['cat', 'dog', 'fish']
word_to_index = {word: idx for idx, word in enumerate(vocab)}

# Function to create a one-hot vector
def one_hot(word):
    vec = np.zeros(len(vocab))
    vec[word_to_index[word]] = 1
    return vec

cat_vec = one_hot('cat')
dog_vec = one_hot('dog')
fish_vec = one_hot('fish')

# Dot products
print(np.dot(cat_vec, dog_vec))   # 0.0
print(np.dot(cat_vec, fish_vec))  # 0.0

# Euclidean distances
print(np.linalg.norm(cat_vec - dog_vec))   # 1.414...
print(np.linalg.norm(cat_vec - fish_vec))  # 1.414...