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Vector Problem

  1. Sep 15, 2004 #1
    Vector Problem URGENT

    Two vectors A and B have precisly equal magnitudes. In order for the magnitude of A +B to be larger then the magnitude of A - B by the factor n, what must be the anle between them?

    There is the question i need help on this quickly thank you for nehelp i know u have to use the cosine rule
     
  2. jcsd
  3. Sep 15, 2004 #2
    Have you worked out the magnitudes of A+B and A - B ?
     
  4. Sep 15, 2004 #3
    no there not given you just know they are equal
     
  5. Sep 15, 2004 #4
    I didn't mean the magnitudes of the original vectors. Let's say |A|=|B|=1 (the answer shouldn't depend on this number). If you let C = A+B and D = A-B , what are the magnitudes of C and D? Hint: to get the magnitude of an arbitrary vector, you take its dot product with....
     
  6. Sep 15, 2004 #5
    sorry i still dont get it you must think im stupid but i really have no idea how this will get a solution
     
  7. Sep 15, 2004 #6

    wm

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    the angle is twice the angle whose tan is 1/(n+1)

    the angle is twice the angle whose tan is 1/(n+1).
     
    Last edited: Sep 15, 2004
  8. Sep 15, 2004 #7
    Please tell me how you got that thank you so much.
     
  9. Sep 15, 2004 #8

    wm

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    Let o be the desired angle; let the magnitudes of A and B be |A| = a and |B| = b; then let a and b = r, the radius of a circle. So |A-B| is the related chord of the circle: c = 2rsin(o/2). And |A+B| is twice the distance from the centre of the circle to the midpoint of the chord (call it x): x = rcos(o/2) =(n+1)c/2 [because you want |A+B| = (n+1)|A-B|]. So c/x = 2tan(o/2) = 2/(n+1); whence o = 2tan^(-1) [1/(n+1)]. I hope!

    PS: Note that I've read the question fairly strictly -- perhaps too strict?
    "In order for the magnitude of A +B to be larger then the magnitude of A - B by the factor n"

    To me this is not the same as saying:
    "In order for the magnitude of A +B to be n-times the magnitude of A - B." If that's what you meant then its 1/n you use.
     
    Last edited: Sep 15, 2004
  10. Sep 15, 2004 #9
    Thank you * infinity
     
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