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Math Help - [SOLVED] Can vector be broken down to components?

  1. #1
    Walter
    Guest

    [SOLVED] Can vector be broken down to components?

    Hi. Here is the URL with some examples: Basic Vector Operations , bottom of the page.
    Suppose we have four vectors (A, B, C, D). We know their magnitudes and angles (directions). We add them and produce a new vector R. Let's consider a different situation. Let's say we are given only the resulting vector R (magitude and angle) and number of vectors (4) added to generate the R vector. Can we determine magnitudes and angles of these individual vectors (all of which are unknown)? Thanks.
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  2. #2
    MHF Contributor

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    Is this what you mean?
    The vector <1,-2,5> is the result of<3,4,0>+<-1,-6,2>+<-1,0,3>.
    BUT ALSO, <1,-2,5>=<1,0,0>+<0,-2,0>+<0,0,5>.
    Any given vector in R^3 is the linear sum of infinitely many three-element sets of vectors. So I think the answer to your question is no.

    If you mean something else, please explain.
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