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Math Help - Angle between 2 vector

  1. #1
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    Angle between 2 vector

    Question : If 2 \theta is the angle between the 2 unit vectors \bar a and \bar b, then show that |\bar a - \bar b| = 2 sin \theta
    -----------------------------------------------------------------------
    Solution:

    I know \bar a - \bar b = |\bar a ||\bar b| cos \theta


    Is dont know what to do afterwards???
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by zorro View Post
    Question : If 2 \theta is the angle between the 2 unit vectors \bar a and \bar b, then show that |\bar a - \bar b| = 2 sin \theta
    -----------------------------------------------------------------------
    Solution:

    I know \bar a - \bar b = |\bar a ||\bar b| cos \theta


    Is dont know what to do afterwards???
    Draw a diagram then it is simple geometry.

    CB
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  3. #3
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    CB i dont know how to draw a diagram with so little ......

    angle is 2 tita how should i dram that.........
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  4. #4
    Senior Member Shanks's Avatar
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    Notice that
    \left|\bar a-\bar b\right|^2=<\bar a-\bar b,\bar a-\bar b>
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  5. #5
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    Dear zorro,
    This is a method which does not require any geometrical drawing. But I think sometimes you will find this method an interesting one. Sorry,I did'nt have time to type the answer. If you have any questions please don't hesitate to ask me.
    Attached Thumbnails Attached Thumbnails Angle between 2 vector-dsc02405.jpg  
    Last edited by Sudharaka; December 29th 2009 at 04:42 AM.
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  6. #6
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    Hello zorro
    Quote Originally Posted by zorro View Post
    CB i dont know how to draw a diagram with so little ......

    angle is 2 tita how should i dram that.........
    Have a look at the attached drawing.

    Since \textbf{a} and \textbf{b} are unit vectors, |PQ| = |PS| = 1, and |\textbf{a}-\textbf{b}| = |QS|.

    Can you complete it now?

    Grandad
    Attached Thumbnails Attached Thumbnails Angle between 2 vector-untitled.jpg  
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  7. #7
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    Thanks Sudharaka and grandad and also every one for ur answer.....
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