first of all assume that I dont have proper math knowledge. I came across this idea while I was studying last night so I need to verify if it's valid, true, have sense etc. orthogonality of function is defined like this: https://en.wikipedia.org/wiki/Orthogonal_functions I wanted to understand concept a bit further so I came across the explanation that says dot product of two functions is almost the same (or similar?) thing as dot product of two vectors, but I didn't knew how to visualize that multiplication of two functions "inside integral" (I assume it's dot product of two functions) to understand it. I assume inside integral should be something like cos(theta) where theta is angle between two functions, but than I got to a conclusion when you usually/always plot graphs of functions for example in 2D coordinate system functions are always/usually "parallel" to one another so cos(theta)=cos(0)=1. I remember from physics class that any point in coordinate system could be represented by a vector of position so I got an idea, can we just "transform" that integral like this: let y(x)=any function ex. sin(x) and g(x)=any function ex. cos(x), a→ be position vector for every point of function y(x), and b→ be position vector for every point of function g(x). can we define orthogonality like this: if the sum of all dot products of position vectors a→ and b→ for every instant, on some interval is zero than functions that those two vectors represent are orthogonal. (sorry for poor vector notation) thank you!