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all right so what Iamp;#39;m going to do in this example is weamp;#39;re 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 letamp;#39;s say we have something like this this is U and this is some vector V then this vector is u minus V yeah so thatamp;#39;s what weamp;#39;re 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 weamp;#39;re squaring that whatamp;#39;s the magnitude of U well thatamp;#39;s just using the magnitude formula we get X 1 square plus y 1 square the mag