3.3 - 3.3 Dot Product Projections By the angle between u...

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§3.3Dot Product; ProjectionsBy theanglebetween~uand~v, we shall mean the angleθdeter-mined by~uand~vthat satisfies0θπ.1
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FormulaGivenP(u1,u2,u3)andQ(v1,v2,v3), by thelaw of cosines,we have||-→PQ||2=||~u||2+||~v||2-2||~u||||~v||cosθThen||~u||||~v||cosθ=12(||~u||2+||~v||2-||-→PQ||2)Hence~u·~v=12(||~u||2+||~v||2-||~u-~v||2)3
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