Definition of the Dot Product

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.)

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