Fundamental data science question — Why |a||b|cos(x)=x1y1+x2y2?

Sep 10, 2023

2 Intuitive ways to prove.

With the growth of generative AI and chatGPT. I discussed some questions about machine learning with a DS friend. when we talked about vectors and similarity, then we talked about dot products. so my fundamental math question is:

why is the dot product of 2 vectors which means the length of 2 vectors * cos(the angle between them) = (x1*y1+x2*y2)?

He explained in 2 ways, both easy to understand. (only need high school math)

#1 Cosine law

#2 Start from definition

That’s it. thanks for reading.




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