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so today I saw a comment on a YouTube video that was requesting a proof of the dot product using the definition so I decided to do a short video explaining why the dot product which seems obvious to us who have taken calculus or know anything about vectors but you know why is that product formula what it is so today Iamp;#39;m going to briefly explain a geometric proof so the dot product here weamp;#39;re interpreting geometrically is this formula which is a dot B equals the magnitude of a times magnitude of B times cosine of theta where theta is the angle between the two vectors so for the purpose of this proof Iamp;#39;m considering a as a vector by itself and be as a vector by itself and theta sub a is this angle here and theta sub B is this angle here which you will see later on so for the for the purpose of this proof it is useful to consider what Iamp;#39;ll call a sub X a sub y b sub X and B sub y so a sub X is just going to be the length of this Iamp;#39;ll here along the