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Vectors questions

  1. May 31, 2009 #1
    1. The problem statement, all variables and given/known data
    Ok I did all the chapter 3 questions in Fundamentals of Physics, but I could not get 2 of them.

    53. Two vectors A and B have precisely equal magnitudes. For the magnitude of A+B to be 100 times greater that the magnitude of A-B, what must be the angle between them?

    54. Two vectors A and B have precisely equal magnitudes. For the magnitude of A+B to be n times greater that the magnitude of A-B, what must be the angle between them?

    2. Relevant equations
    Law of Cosines.

    3. The attempt at a solution
    I am pretty sure the angle has to be small for 53. I know that the magnitude of A is equal to the magnitude of B. Using the Law of Cosines I get cos:smile:=1-mag(A-B)/2A^2. For A+B I get cos:tongue:=1-50mag(A-B)/A^2. 180-cos:tongue:=cos:smile:. I don't know where to go after this. I messed around with the equations, but I can't ever get rid of A or B. The second one I have not tried yet, because if I can't the first, then how am I supposed to get the second. THANKS for the help!
     
  2. jcsd
  3. May 31, 2009 #2
    Do you know the parallelogram geometric view of addition and subtraction of vectors? Note that in the case that all four sides are equal, you are dealing with a rhombus, for which the diagonals bisect each other in a right angle.
     
  4. May 31, 2009 #3
    Oh got it so, that makes a right triangle with legs 50mag(A-B) and another leg mag(A-B)/2. aTan(1/100)=.5729. Doubling that i get 1.1458 degrees. Right?

    For the second one I get aTan(1/n). Right?

    Thanks slider142!
     
  5. May 31, 2009 #4
    Yep. Good job!
     
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