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all right so what Im going to do in this example is were going to derive the the formula for u dot V naught as u dot V equals the magnitude of U times the magnitude of V times the cosine of the angle between the two vectors how do we get where does this come from it comes from one of the formulas the the law of cosines so the law of cosine just using the law of cosine formulas we have this maybe I should draw a little picture here if we have you and we have V lets say we have something like this this is U and this is some vector V then this vector is u minus V yeah so thats what were looking at so what is the magnitude of U minus V while the magnitude squared the magnitude is the square root of a u minus V X 1 minus X 2 squared plus y 1 minus y 2 squared so that is the magnitude but then were squaring that whats the magnitude of U well thats just using the magnitude formula we get X 1 square plus y 1 square the magnitude of V and then this is squared the magnitude of V is the s
