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Calculating the magnitude of two vectors

  1. Sep 20, 2013 #1
    1. Two displacement vectors, S and T, have magnitudes S = 3 m and T= 4 m. Which of the following could be the magnitude of the difference vector S - T ? (There may be more than one correct answer.) (i) 9 m; (ii) 7 m; (iii) 5 m; (iv) 1 m; (v) 0 m; (vi) - 1 m



    2. Vector principles



    3. shouldn't this problem tell me the direction of the vectors? the magnitude of the resultant vector is not always the sum or difference of the magnitude of the vectors unless they are parallel!
     
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  3. Sep 20, 2013 #2

    mfb

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    It does not have to. The problem statement does not ask about the actual magnitude, it just asks what is possible.
    Right, but you can still say something about the possible values for the magnitude of the difference.
    Can you have two vectors with a magnitude of 1 each, where the difference has a magnitude of 1000?
     
  4. Sep 20, 2013 #3
    no i don't think that's possible, but i have a side question to make sure i understand what i read in my textbook, then i will try to solve this problem, if i have a displacement vector of magnitude 1km north, then another 2km east, adding the two will result in a vector 63 degrees east of north with magnitude = square root of 5, but what if i wanna subtract the two vectors, i will have to flip vector 1 km then slide it so that it's tail lies on the head of vector 2km, then again the resultant vector's magnitude is going to be square root of 5, is that correct? how come the addition and the subtraction of two right angle vectors have the same magnitude?!
     
  5. Sep 20, 2013 #4

    mfb

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    Correct.

    This is special for orthogonal vectors - flipping the sign of one vector is like mirroring the whole setup, and mirroring does not change lengths (magnitudes) of vectors.
     
  6. Sep 20, 2013 #5
    well then it should be 7 m because as far as i can understand the magnitude doesn't depend on whether it's addition or subtraction, the direction is what changes correct? and the magnitude should be close to the sum of the magnitude of the two vectors correct?
     
  7. Sep 20, 2013 #6

    mfb

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    In general, it does.
    Why should it be close to the sum?

    Did you consider some examples, like
    S=(0,1), T=(1,0)
    S=(5,2), T=(4,2)
    S=(5,0), T=(-4,0)
    ...? This will help to get a feeling for the problem.
     
  8. Sep 20, 2013 #7
    T=(-4.0) my text book says that the magnitude is never negative! and sorry but i gave it everything that i have, i don't see any difference between what u said above and the problem, the problem remains i can't tell unless the vectors are drawn! can u plz explain the answer to me?
     
  9. Sep 20, 2013 #8

    mfb

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    My examples are vectors (in 2D), not magnitudes of vectors.
    You can draw them on a plane, if you like.

    Good, so you already excluded one of the possible answers.
     
  10. Sep 20, 2013 #9
    oh those are coordinates, ok i will draw them and add and subtract and see how it goes!
     
  11. Sep 20, 2013 #10
    ok i did them, i'm not really sure what to make of it!!!! more hints plz
     
  12. Sep 20, 2013 #11

    mfb

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    Please show your results then.

    What did you get for S-T? Which magnitudes did you get for S, T and S-T?
     
  13. Sep 20, 2013 #12
    S=(5,2), T=(4,2) magnitude = 1
    S=(0,1), T=(1,0) magnitude = square root of 2
    S=(5,0), T=(-4,0) magnitude = 9

    i can't find any relationship between the magnitude of the vectors and the magnitude of the difference vector
     
  14. Sep 20, 2013 #13

    mfb

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    Where are the magnitudes of S and T?
    There is no fixed relationship, that is the important result. There are lower and upper bounds, however. Take two straight objects with a very different length, put them on your desk (such that their ends touch) and see which length between the non-touching ends you can get. What is the maximum, what is the minimum?
     
  15. Sep 20, 2013 #14
    i'm sorry i don't have a ruler with me atm, and i have a lot to go through still, i should finish this vectors chapter, plus another chemistry chapter :( more hints plz
     
  16. Sep 20, 2013 #15

    arildno

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    Do you remember the..law of cosines?

    Think a bit about how your question might be related to that..
     
  17. Sep 20, 2013 #16
    i know the law of cosines, there are no angles or anything that i could use, guyz why are u making this so difficult, plz spill the beans :(
     
  18. Sep 20, 2013 #17

    arildno

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    Now, think geometrically about vectors S, T, S-T

    What sort of geometrical SHAPE will these typically look like when you draw them?

    Hint: Draw S and T both from the origin. Where will you find S-T?
     
  19. Sep 20, 2013 #18
    they could be a straight line, they could be a triangle, they could be anything
     
  20. Sep 20, 2013 #19

    arildno

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    Anything? When you add them vectorially?

    The basic case is that of a TRIANGLE, with two extreme cases as straight lines.

    Agreed?

    Now, how can you, in the general case of the triangle compute the length of S-T? What formula would you use?
     
  21. Sep 20, 2013 #20
    ok drawing some random vectors, making a triangle, applying the law of cosines, i reached that the difference vector is equal to the square root of (25-24cos theta) so the magnitude of the vector depends on the theta obviously and there's no way to tell the magnitude without knowing more information
     
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