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Sum of vector

  1. Jan 18, 2014 #1
    1. The problem statement, all variables and given/known data

    The sum of two vectors, A→ + B→, is perpendicular to their difference, A→ - B→. How do the vectors magnitude compare?


    3. The attempt at a solution

    SQRT[(A+B)^2 + (A-B)^2]
     
  2. jcsd
  3. Jan 18, 2014 #2
    Have you studied the scalar (dot) product of vectors?
     
  4. Jan 18, 2014 #3
    I have but only very briefly-1 lecture class on that and that was 1 semester back. But, if you could give me a rough overview, I'll build on those knowledge.
     
  5. Jan 18, 2014 #4

    BvU

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    What does perpendicularity mean for the dot product ? write it out as a vector expression, then use the distributive property of the dot product.
     
  6. Jan 18, 2014 #5
    It means A→.B→ = 0
     
  7. Jan 18, 2014 #6

    BvU

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    Right. Now A+B is perpendicular to A-B, so: (A+B).(A-B)=0
     
  8. Jan 18, 2014 #7
    Dot product implies that the product of two vector A→.B→ = 0

    Let A→+B→ = R1 [itex]\wedge[/itex] A→-B→= R2

    R1.R2 = 0

    (A→+B→).(A→-B→) = A^2→ - B^2→ = 0

    A=B
     
  9. Jan 18, 2014 #8

    BvU

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    Bingo.
     
  10. Jan 18, 2014 #9
    See, it was not that hard :)
     
  11. Jan 18, 2014 #10
    It wasn't but my interpretation was different. I went in with the assumption
    1) A right angle triangle exists.
    2) the length parallel to the y-axis = r1
    3) length perpendicular to r1 = r2
    4) find the resultant
     
  12. Jan 18, 2014 #11
    I do not understand how your assumption is related to the problem.
     
  13. Jan 18, 2014 #12
    I interpreted the question wrongly and build assumptions on the wrong premise.
     
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