[Solved] Given two word embeddings:embedding_king = [0.5, 0.8, 0.1]embedding_queen = [0.45, 0.75, 0.15]What is the cosine similarity between them (rounded to 2 decimals)? | NLP

NLP - Word Embeddings

Given two word embeddings:
embedding_king = [0.5, 0.8, 0.1]
embedding_queen = [0.45, 0.75, 0.15]
What is the cosine similarity between them (rounded to 2 decimals)?

A0.99

B0.85

C0.75

D0.65

Step-by-Step Solution

Solution:

Step 1: Calculate dot product of vectors
Dot product = (0.5*0.45) + (0.8*0.75) + (0.1*0.15) = 0.225 + 0.6 + 0.015 = 0.84
Step 2: Calculate magnitudes and cosine similarity
Magnitude king = sqrt(0.5² + 0.8² + 0.1²) = sqrt(0.25 + 0.64 + 0.01) = sqrt(0.9) ≈ 0.95
Magnitude queen = sqrt(0.45² + 0.75² + 0.15²) = sqrt(0.2025 + 0.5625 + 0.0225) = sqrt(0.7875) ≈ 0.89
Cosine similarity = 0.84 / (0.95 * 0.89) ≈ 0.84 / 0.8455 ≈ 0.99
Final Answer:
0.99 -> Option A
Quick Check:
Cosine similarity ≈ 0.99 [OK]

Quick Trick: Cosine similarity near 1 means vectors are very similar [OK]

Common Mistakes:

MISTAKES

Forgetting to divide by magnitudes
Mixing up dot product with Euclidean distance
Rounding errors in calculation

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Given two word embeddings:

Step 1: Calculate dot product of vectors

Step 2: Calculate magnitudes and cosine similarity

Final Answer:

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