NLP - Text Similarity and Search
Given vectors
A = [1, 2, 3] and B = [4, 5, 6], what is the cosine similarity (rounded to 2 decimals)?Given vectors A = [1, 2, 3] and B = [4, 5, 6], what is the cosine similarity (rounded to 2 decimals)?
medium📝 Predict Output Q13 of 15
Step-by-Step Solution
Solution:
Step 1: Calculate dot product of A and B
Dot product = 1*4 + 2*5 + 3*6 = 4 + 10 + 18 = 32Step 2: Calculate norms of A and B
Norm A = sqrt(1^2 + 2^2 + 3^2) = sqrt(14) ≈ 3.74; Norm B = sqrt(4^2 + 5^2 + 6^2) = sqrt(77) ≈ 8.77Step 3: Compute cosine similarity
Cosine similarity = 32 / (3.74 * 8.77) ≈ 32 / 32.83 ≈ 0.9749 rounded to 0.97Step 4: Check closest option
0.97 matches the value rounded to 2 decimals.Final Answer:
0.97 -> Option AQuick Check:
Dot product / (norms product) ≈ 0.97 [OK]
Quick Trick: Calculate dot product and divide by product of lengths [OK]
Common Mistakes:
MISTAKES- Forgetting to take vector norms
- Mixing up dot product with element-wise multiplication
- Rounding too early causing wrong answer
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