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- TL;DR Summary
- Dot Product Multiplication Meaning

I'm confused about what we are really measuring when taking the dot product of two vectors. When we say we are measure "how much one vector points in the direction of the other", that description is not clear. At first I thought it meant how much of a shadow one vector casts on another and I thought this was the same as finding the adjacent side of a triangle where we'd just multiply cosine by the hypotenuse. But I'm not sure what we are doing in using the dot product formula where we multiply corresponding vector points and then add the products together. E.g. take vectors A and B where A = (3,0) and B = (6,8). Had B been instead = to (3,4) then B would be like the hypotenuse of a right 3,4,5 triangle forming over A where A is the adjacent (base) side of the triangle. When B = (6,8) it's like we doubled the length of B from when it was (3,4). The dot product of A and B is now (3x6) + (0x8) = 18.

What exactly does 18 represent? B does not go 6 times further to the right then A did. It only went twice as far to the right. Why are we even multiplying the two together? Thanks

What exactly does 18 represent? B does not go 6 times further to the right then A did. It only went twice as far to the right. Why are we even multiplying the two together? Thanks