[Solved] Given two vectors A = [2, 2, 1] and B = [1, 0, 1], what is the cosine similarity... Given two vectors A = [2, 2, 1] and B = [1, 0, 1], what is the cosine similarity computed by the code below? | NLP

NLP - Text Similarity and Search

Given two vectors A = [2, 2, 1] and B = [1, 0, 1], what is the cosine similarity computed by the code below? import numpy as np A = np.array([2, 2, 1]) B = np.array([1, 0, 1]) cos_sim = np.dot(A, B) / (np.linalg.norm(A) * np.linalg.norm(B)) print(round(cos_sim, 2))

A0.71

B0.75

C0.50

D0.85

Step-by-Step Solution

Solution:

Step 1: Calculate dot product
dot(A,B) = 2*1 + 2*0 + 1*1 = 2 + 0 + 1 = 3.
Step 2: Calculate norms and cosine similarity
norm(A) = sqrt(2²+2²+1²) = sqrt(4+4+1) = sqrt(9) = 3; norm(B) = sqrt(1²+0+1²) = sqrt(2) ≈ 1.414.
Cosine similarity = 3 / (3 * 1.414) ≈ 3 / 4.242 ≈ 0.707; round(0.707, 2) = 0.71.
Final Answer:
0.71 -> Option A
Quick Check:
Cosine similarity calculation = 0.71 [OK]

Quick Trick: Calculate dot product and divide by product of norms [OK]

Common Mistakes:

MISTAKES

Forgetting to take vector norms
Incorrect dot product calculation
Rounding errors

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More NLP Quizzes

Given two vectors A = [2, 2, 1] and B = [1, 0, 1], what is the cosine similarity computed by the code below?

Step 1: Calculate dot product

Step 2: Calculate norms and cosine similarity

Final Answer:

Quick Check:

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