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Math Help - Easy Vector Question

  1. #1
    Super Member craig's Avatar
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    Easy Vector Question

    Alright this seems a pretty easy vector question, just wondering if it's me or the solutions I've got that are wrong.

    If P and Q are the points with position vectors p = −i+3j+2k and q = i−7j+4k respectively, find the position vector of the mid-point of the line PQ.
    First I found the line PQ, this is equal to q-p which can easily be calculated to be 2x-10y+2z. The midpoint is just half of this which is x-5y+z.

    In the solutions however they have used p+q to calculate the line PQ, is there something obvious I'm missing?

    Thanks in advance to the person who sorts this annoying little problem out for me
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  2. #2
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    q-p is a relative vector for the path from p to q. It is not a position vector for anything on that line, unless you pick one that is.

    Look at it in one dimension.

    p = 5
    q = 2

    (5-2)/2 = 3/2 = 1.5 -- That can't be half way between 2 and 5

    (5+2)/2 = 7/2 = 3.5 -- That is half way between 2 and 5.

    Don't you have a definition of a "position vector"? Something about beginning at the Origin should come to mind.
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  3. #3
    Super Member craig's Avatar
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    Ahh I see, thank you.
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