BitWithBite
AI & Machine Learning Worksheet
🤖 Vector Operations
SCORE___ / 20
NameClassDate
After this worksheet you can
Add and scale vectorsDot productNorms (length)Cosine similarity idea📚 Quick Recap
If this entire course track has one single most-used piece of math, it's the dot product. It's the operation underneath linear regression (Module 7), the core computation inside every neural network layer (Tier 3), and the way similarity gets measured in search and recommendation systems (Tier 2 and Tier 4). Understanding it well here pays off constantly later.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1[1,2] + [3,4] =:
2Dot product of [1,2] and [3,4]:
3The L2 norm of [3,4] is:
4Dot product of perpendicular vectors is:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
52 * [1,3] = [2, ].
6Dot product multiplies pairwise then .
7Compute [2,1].[4,3].
8Norm of [6,8]?
9Why does ML use dot products constantly?
🚀 Section C · Challenge ● CHALLENGE 5
10Two docs as vectors - how tell similarity?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 6 6 sums/adds 7 = 2*4 + 1*3 = 11 8 = sqrt(36+64) = 10 9 = Neuron outputs, similarities, projections are all dot products | 10 = Cosine similarity of their embedding vectors