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Resultant of two vectors of equal magnitude

  1. Aug 16, 2016 #1
    1. The problem statement, all variables and given/known data

    Resultant of two vectors of equal magnitude A is
    a) √3 A at 60
    b) √2 A at 90
    c) 2A at 120
    d) A at 180
    2. Relevant equations
    When two vectors are of equal magnitudes then their resultant is
    ##A_R## = 2 A Cos θ/2
    3. The attempt at a solution
    I think we need more information especially the angle between the given two vectors . Or we can eliminate options one by one. Answer is both a & b
    I tried to cross check it . If the resultant is at 60 it means angle between the vectors we started with is 120 i.e θ =120
    if we plug in the numbers
    ##A_R## = 2A Cos 120/2
    = 2A cos 60
    = 2A 1/2
    = A
    which is not equal to √3
    Similarly for option b
    ##A_R## = 2A Cos 180/2
    = 2A cos 90
    = 2A 0
    = 0
    I 'll get it correct if I directly put θ=60 & 90 respectively . But as far as I know θ in this formula ##A_R## = 2 A Cos θ/2 is angle between the two vectors and not the vector and resultant
     
  2. jcsd
  3. Aug 16, 2016 #2

    cnh1995

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    Homework Helper

    Right. The question doesn't make sense.
     
  4. Aug 16, 2016 #3
    I think you are right - that the angles shown in the problem statement are the original angles between the 2 vectors of magnitude A.
     
  5. Aug 16, 2016 #4

    Student100

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    Education Advisor
    Gold Member

    I don't see the problem, it seems to me it's giving you the angles between the two vectors to check and what the resultant magnitude should be, so A and B are both correct as you say.
     
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