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Math Help - Vector magnitude addition

  1. #1
    M.R
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    Vector magnitude addition

    I hope this is the right forum.

    The question is about vector addition. Suppose you have two vectors:

    u=<1,1,1>, v=<-1,2.1>

    The magnitudes are:

    ||u+v||=\sqrt{13} and

    ||u|| + ||v|| = \sqrt{3} + \sqrt{6}

    But the answer in the back of the book is showing \sqrt{13} for both? Where am I going wrong?
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  2. #2
    MHF Contributor
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    Re: Vector magnitude addition

    I agree with your answers. Moreover, in a euclidean space, \|u+v\| = \|u\|+\|v\| iff u and v are proportional, which is not the case here. There is probably a typo in the book.
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  3. #3
    MHF Contributor Reckoner's Avatar
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    Re: Vector magnitude addition

    Quote Originally Posted by M.R View Post
    But the answer in the back of the book is showing \sqrt{13} for both? Where am I going wrong?
    I think you are correct, assuming I am reading your work correctly.

    \mathbf u = \langle1,1,1\rangle, \mathbf v = \langle-1,2,1\rangle

    \|\mathbf u + \mathbf v\| = \|\langle0,3,2\rangle\| = \sqrt{13}

    \|\mathbf u\| + \|\mathbf v\| = \sqrt3 + \sqrt6

    \sqrt{13}\neq\sqrt3+\sqrt6
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  4. #4
    M.R
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    Re: Vector magnitude addition

    Thank you both for the verification.

    BTW, where is the thanks button?
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  5. #5
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    Re: Vector magnitude addition

    Apparently. in order for the Thanks button to be visible, the mouse pointer has to be located on the post.

    Vector magnitude addition-thanks.png
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  6. #6
    M.R
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    Re: Vector magnitude addition

    Yes, it appears on the bottom right hand corner. I liked the old system better though.
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