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Math Help - Basic vector help

  1. #1
    Senior Member Paze's Avatar
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    Basic vector help

    Hey MHF.

    I'm learning vectors now and I have 2 questions.

    How come this is true: Basic vector help-su58k01_m05.gif

    To me, this is not very intuitive. If I have a triangle, the sides do not add up to become the 3rd side as displayed but I'm guessing there is some other factor at play to make this a logical conclusion.

    My other question is if there are any videos on khan academy or any sites like that covering this concept? I have searched on Khan but to no avail...He starts discussing vectors in linear algebra but I'm pretty sure this is taught before linear algebra.

    Thanks!
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  2. #2
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    Re: Basic vector help

    Paze
    It seems to me that you confuse the vectors with the Algebra of segments...
    Consider a triangle ABC. then vector AB+vector BC = vector AC ( the third side....
    However if AB,AC,BC are segments we have the triangle inequality (length of any side )< summ of the lengths of the two other sides) ..
    Please revise the definition of the vectors .
    Thanks from Paze
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  3. #3
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    Re: Basic vector help

    Quote Originally Posted by Paze View Post
    How come this is true: Click image for larger version. 

Name:	Su58k01_m05.gif 
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Size:	12.5 KB 
ID:	27877
    To me, this is not very intuitive. If I have a triangle, the sides do not add up to become the 3rd side as displayed but I'm guessing there is some other factor at play to make this a logical conclusion.

    Do you understand that a vector is an equivalence class of 'objects' that have a given length and a given direction?

    Look at the vector \vec{a}. It has those two properties.

    If you start at point B and 'put' two \vec{a} you are at point K.
    Then 'move off as one \vec{b} you end up at point M

    Thus 2\vec{a}+\vec{b} is the vector \vec{BM}

    Now, there is no real triangle that at all. You see the combination of two vectors is a vector.
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  4. #4
    Senior Member Paze's Avatar
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    Re: Basic vector help

    I do understand that they have a given length and a given direction. Is there a simple way to envision this? Like maybe...

    Is this also true for my example/picture if I make some assumptions, namely that segment (can I call it segment?) BK is 30 and segment BM is 45. BK is 2 kilometers, KM is 1.5 kilometers and BM is thus 3.5 kilometers?

    A car starts driving 30 north-east from point B. It drives for 2 kilometers and then takes a sharp turn east and drives for 1.5 kilometers.

    The car has driven equally to 3.5 kilometers 45 north-east from its starting point (point B).
    Last edited by Paze; April 9th 2013 at 02:32 PM.
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  5. #5
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    Re: Basic vector help

    Quote Originally Posted by Paze View Post
    I do understand that they have a given length and a given direction. Is there a simple way to envision this? Like maybe...Is this also true for my example/picture if I make some assumptions, namely that segment (can I call it segment?) BK is 30 and segment BM is 45. BK is 2 kilometers, KM is 1.5 kilometers and BM is thus 3.5 kilometers?
    A car starts driving 30 north-east from point B. It drives for 2 kilometers and then takes a sharp turn east and drives for 1.5 kilometers. The car has driven equally to 3.5 kilometers 45 north-east from its starting point (point B).
    You have a too literal view of vectors.
    They may represent physical objects but vectors are not physical objects.

    Here is a good textbook: A vector Space Approach to Geomentry by Melvin Hausner.
    It is a Dover reprint, so not expensive.
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  6. #6
    Senior Member Paze's Avatar
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    Re: Basic vector help

    Thank you. I'll have a look at that!
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