Definition of the Dot Product

Given two vectors V and W, suppose they are represented by the coordinates a = (x_a, y_a) and b = (x_b, y_b). (Place tails of V and W at the origin. Then their heads are at a = (x_a, y_a) and b = (x_b, y_b).)

Definition: The dot product of V and W is defined to be VW = x_a*x_b + y_a*y_b

It's hard to see what the dot product is good for at this stage of the game. We'll work on it. One important thing ... What's VV?

VV = x_a² + y_a², but that's just the length of V squared - VV = |V||V|

(See, dot products are good for something.)