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Math Help - vectors

  1. #1
    MHF Contributor Quick's Avatar
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    vectors

    I would like to know what the i,j,k stand for in things like:
    v=2i+j-k

    my guess: they stand for north, east, and ?forward?
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    Quote Originally Posted by Quick
    I would like to know what the i,j,k stand for in things like:
    v=2i+j-k

    my guess: they stand for north, east, and ?forward?
    They are unit vectors parallel to the coordinate axes, usualy \bold{i}=[1,0,0],\ \bold{j}=[0,1,0],\ \bold{k}=[0,0,1]

    RonL
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    Quote Originally Posted by Quick
    I would like to know what the i,j,k stand for in things like:
    v=2i+j-k

    my guess: they stand for north, east, and ?forward?
    Firstly,
    it is \bold{i} not i, if you are writing on paper and do not want to draw a bold line you write \vec{i} (with an arrow on top).

    Let me explain it differently.
    This is a vector,
    \bold{v}=2\bold{i}+\bold{j}-\bold{k}
    where, \bold{i},\bold{j},\bold{k} are called vector-components.

    Basically you are in 3 dimensions. Instead of 2 (xy graph) you know have an xyz graph. So think of a point located at (2,1,-1) now from that point draw a line to the orogin (0,0,0) the resulting line would be called a vector defined by 2\bold{i}+\bold{j}-\bold{k}
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    Quote Originally Posted by ThePerfectHacker
    Firstly,
    it is \bold{i} not i, if you are writing on paper and do not want to draw a bold line you write \vec{i} (with an arrow on top).

    Let me explain it differently.
    This is a vector,
    \bold{v}=2\bold{i}+\bold{j}-\bold{k}
    where, \bold{i},\bold{j},\bold{k} are called vector-components.

    Basically you are in 3 dimensions. Instead of 2 (xy graph) you know have an xyz graph. So think of a point located at (2,1,-1) now from that point draw a line to the orogin (0,0,0) the resulting line would be called a vector defined by 2\bold{i}+\bold{j}-\bold{k}
    so then \bold{i} would be the x-coordinate, \bold{j} would be y, and \bold{k} would be z

    and the distance and direction between that point and the origin is the vector? seems logical to me
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    Quote Originally Posted by Quick
    so then \bold{i} would be the x-coordinate, \bold{j} would be y, and \bold{k} would be z

    and the distance and direction between that point and the origin is the vector? seems logical to me
    Look what CaptainBlank said. Yes, if that is what you mean.
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  6. #6
    MHF Contributor Quick's Avatar
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    just a question about directions...

    would I consider the y axis as elevation, like if I said the ball was thrown upward at 3 ft/s would be 0\bold{i}+3\bold{j}+0\bold{k}

    would I consider the z axis moving forward, like If I said that a man walks forward at a pace of 1 ft/s would be 0\bold{i}+0\bold{j}+1\bold{k}
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    Quote Originally Posted by Quick
    so then \bold{i} would be the x-coordinate, \bold{j} would be y, and \bold{k} would be z

    and the distance and direction between that point and the origin is the vector? seems logical to me
    The coefficients of \bold{i} would be the x-coordinate (etc) for
    a position vector, \bold{i} itself is the unit vector parallel to the
    x-axis.

    RonL
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