Results 1 to 2 of 2

Thread: Prove Cosine law using vectors!

  1. #1
    Newbie
    Joined
    Jun 2012
    From
    Where you least expect
    Posts
    10

    Prove Cosine law using vectors!

    If C (dot) C= IC^2I how can I prove cosine law with vectors?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Reckoner's Avatar
    Joined
    May 2008
    From
    Baltimore, MD (USA)
    Posts
    1,024
    Thanks
    76
    Awards
    1

    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:

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

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

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

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

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

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

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

    Now just finish it up.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Jun 22nd 2011, 12:43 PM
  2. Cosine between two vectors
    Posted in the Algebra Forum
    Replies: 2
    Last Post: Nov 25th 2010, 01:19 AM
  3. prove vectors
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Nov 4th 2009, 03:13 AM
  4. Using calculus to prove cosine inequality
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Dec 23rd 2007, 12:21 PM
  5. Use vectors to prove ...
    Posted in the Calculus Forum
    Replies: 5
    Last Post: Dec 31st 2006, 02:47 PM

Search Tags


/mathhelpforum @mathhelpforum