Given two vectors V and W, suppose they are represented by the coordinates
a = (xa, ya)and b = (xb, yb).(Place tails of V and W at the origin. Then their heads are at a = (xa, ya)and b = (xb, yb).)
Definition: The dot product of V and W is defined to be VW = xa*xb + ya*yb
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 = xa2 + ya2, but that's just the length of V squared - VV = |V||V|
(See, dot products are good for something.)