HUGE takeaway: understanding the push formula is relatively simple, despite its extreme usefulness. Push is used to find the component of a vector in a certain direction. x dot y over y dot y all times y ===I attempt to explain=== The coefficient, x dot y over y dot y, represents a minimum distance. Because you are finding a component... True components are perpendicular. Otherwise they would have components of each other, in themselves!! Because the two components are perpendicular, you can minimize the length of the second one. Geometry FACT. The shortest distance to a line is by movement perpendicular... the longest distance to a line is by movement parallel. How to find the formula? I choose to split x into a comma b, and y into c comma d. Then coordinate geometry a little, then calculus a little. ===others=== The music is Intermezzo 118 2 A Major by Brahms, played by Arthur Rubinstein. Does it take forever to load? Green vectors are tangent, orange vectors are perpendicular. I based the colors off the fact that the circles are blue.
