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Math Help - Prove Cosine law using vectors!

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    Prove Cosine law using vectors!

    If C (dot) C= IC^2I how can I prove cosine law with vectors?
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    Re: Prove Cosine law using vectors!

    Quote Originally Posted by Clairvoyantski View Post
    If C (dot) C= IC^2I how can I prove cosine law with vectors?
    Use this property:

    \mathbf{u}\cdot\mathbf{v}=\left\|\mathbf{u} \right\|\left\|\mathbf{v}\right\|\cos\theta,

    where \theta is the angle between \mathbf{u} and \mathbf{v}.

    Form a triangle with \mathbf{u} and \mathbf{v} as two of its sides. The remaining side is represented by \mathbf{u}-\mathbf{v}. Squaring the length of this side gives

    \left\|\mathbf{u}-\mathbf{v}\right\|^2

    =\left(\mathbf{u}-\mathbf{v}\right)\cdot\left(\mathbf{u}-\mathbf{v}\right)

    =\mathbf{u}\cdot\left(\mathbf{u}-\mathbf{v}\right)-\mathbf{v}\cdot\left(\mathbf{u}-\mathbf{v}\right)

    =\mathbf{u}\cdot\mathbf{u}-\mathbf{u}\cdot\mathbf{v}-\mathbf{v}\cdot\mathbf{u}+\mathbf{v}\cdot\mathbf{v  }\right)

    Now just finish it up.
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