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The angles between vectors?

  1. Feb 25, 2012 #1
    1. The problem statement, all variables and given/known data

    Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A+B to be 120 times larger than the magnitude of A-B , what must be the angle between them?

    2. Relevant equations
    None (i think)


    3. The attempt at a solution
    A+B=120(A-B)
    (xi+yi)+(xi+yi)
    2x+2y=120(2x+2y)
    2x+2y+240x-240y
    Then I dont know where to go from here
    Is what I am doing even correct?
    Point me in the right direction
     
  2. jcsd
  3. Feb 25, 2012 #2

    jedishrfu

    Staff: Mentor

    Have you learned about the vector inner or dot product? Look at its definition and usage.
     
  4. Feb 25, 2012 #3
    No, please explain further
     
  5. Feb 25, 2012 #4
    Draw a right-angled triangle ABC where BC is the hypotenuse, O is the midpoint of BC. You wil see that one of the two other sides is the magnitude of the vector-sum and the other is the magnitude of the vector-difference. A bit of trigonometry would lead you to the answer.
     
  6. Feb 25, 2012 #5
    Could you please expand?
    Like what is the significance of knowing O?,etc
     
  7. Feb 25, 2012 #6

    gneill

    User Avatar

    Staff: Mentor

    You're free to choose whatever coordinate system and initial vector length you want to solve the problem. I might suggest that you choose a unit vector length and place your coordinate system so that one of the vectors lies along one of the coordinate axes. Then the other vector makes angle θ with that axis.
     
  8. Feb 25, 2012 #7
  9. Feb 25, 2012 #8
    yeah, but how is that helpful/relevant?
     
  10. Feb 25, 2012 #9
    Then the angle between vectors a and b is two times the angle between BC and AB, which should be calculated using tangent formula.
     
  11. Feb 25, 2012 #10
    Okay, I am starting to understand.
    so if we name the angle between AB and BC as θ, then we can get it by,
    Tan^-1(a-b/a+b)
    then we multiply the result by 2
    but then... we dont have a and b
    all we know is that lAl=lBl
    How can that help us get a and b?
    Thank you so much btw...you're helping me h=get closer to the answer
     
  12. Feb 25, 2012 #11
    I dont know what you mean?
    can you expand
     
  13. Feb 25, 2012 #12

    gneill

    User Avatar

    Staff: Mentor

    If vector A is a unit vector and lies along the x-axis, then its vector components are (1,0). If vector B makes some angle θ with A, then its vector components must be (cos(θ),sin(θ)). You can thus form A + B and A - B algebraically from those components. Write expressions for the magnitude of each and apply your required relationship between them.

    attachment.php?attachmentid=44375&stc=1&d=1330193482.gif
     

    Attached Files:

  14. Feb 25, 2012 #13
    But the magnitude of the vector-sum is 120 times that of the vector-difference. The tangent formula only requires a RATIO between two sides of the triangle.
     
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