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Math Help - Law of Cosines

  1. #1
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    Law of Cosines

    If  \bold{C} = \bold{A} + \bold{B}

    Then  \bold{C} \cdot \bold{C} = (\bold{A} + \bold{B}) \cdot (\bold{A} + \bold{B})

     |\bold{C}|^{2} = |\bold{A}^{2}| + |\bold{B}^{2}| + 2|\bold{A}||\bold{B}| \cos \theta where  \theta is the angle between the extension of  \bold{A} and  \bold{B} .

    Then this is usually expressed as  C^{2} = A^{2} + B^{2} - 2AB \cos \phi where  \phi is the angle between  \bold{A} and  \bold{B} .

    But why isn't  \bold{C} \cdot \bold{C} = |\bold{C}| ?
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  2. #2
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    Because say \bold{C} = (x,y) then |\bold{C}| = \sqrt{x^2+y^2} and \bold{C}\cdot \bold{C} = x^2+y^2. So you are off by a square root.
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