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.