Given two vectors V and W, suppose they are represented by the coordinatesa = (x _{a},y and_{a})b = (x _{b},y (Place tails of V and W at the origin. Then their heads are at_{b}).a = (x _{a},y and_{a})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

_{a}^{2}+ y_{a}^{2}, but that's just the length of V squared - VV = |V||V|(See, dot products are good for something.)