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Math Help - Subtracting Vectors - Limited Information

  1. #1
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    Subtracting Vectors - Limited Information

    I have no idea how to solve the following problem because there does not seem to be enough information.

    Could anyone point me in the right direction?

    Here is the problem.

    ************************************
    Suppose vector b has magnitude 8 m/s and direction S24degreesW, the direction of vector b - vector c is east and vector |c| is a minimum. Determine the magnitude and direction of vector c, to one decimal place.

    The answer given to this is 7.4 m/s on a bearing of S9degreesE.
    *************************************

    See the diagram below for my understanding of the problem:
    Subtracting Vectors - Limited Information-vector_problem2.jpg

    Any help would be much appreciated.

    Thanks.

    bdika
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  2. #2
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    For starters, the vector \displaystyle \mathbf{b} - \mathbf{c} in your picture is not pointing east, it's pointing west...
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  3. #3
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    Thanks Prove It. I considered the direction wrong but thought that I read somewhere in this forum about the origin of the direction or some such thing. In any case, obviously you are right and thanks for clearing it up for me.

    I have some other thoughts on the problem (see image below) but don't know how to proceed. If you haven't already guessed, I am not a mathematician but a Chartered Accountant by profession who studied these things in university more than 30 years ago and now find myself having to relearn them.

    Subtracting Vectors - Limited Information-vector_problem4.jpg

    I'm sorry if I am completely off base. I would appreciate any help that I can get on this.

    Thanks.

    bdika
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  4. #4
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    First, you need to note that \displaystyle \mathbf{c} = \mathbf{b} - (\mathbf{b} - \mathbf{c}) = \mathbf{b} + [-(\mathbf{b} - \mathbf{c})].

    Now that you have your \displaystyle \mathbf{b} - \mathbf{c} pointing in the right direction, you need to reverse its direction, then perform the vector addition, see the following pic...



    Now try to fill in as many missing lengths and angles in your triangle, see where you can go from there...
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  5. #5
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    Quote Originally Posted by Prove It View Post
    vector c should point the other way, correct?
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  6. #6
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    Quote Originally Posted by skeeter View Post
    vector c should point the other way, correct?
    Yes it should, my apologies...
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  7. #7
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    Hi Prove It

    Thanks for the reply.

    However I can't seem to locate the picture that you mentioned in the quote below:

    Now that you have your pointing in the right direction, you need to reverse its direction, then perform the vector addition, see the following pic...
    ...or were you referring to my second diagram?

    Thanks

    bdika
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  8. #8
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    No, it's directly underneath the text... Maybe you should refresh your browser...
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  9. #9
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    Thanks Prove It

    The picture shows up in my browser at home (Firefox) but not in the browser at work (Internet Explorer). In any case, I have seen the picture and have access to it.

    I will work on solving it, and report back my progress.

    Thanks.

    bdika
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