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Playing with Vectors

  1. May 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Q1)
    Let vector B = (5.00m, 65°), let the magnitude of vector C equal (=) the magnitude of vector A, and C has a direction 20° greater than vector A.
    A(dot/scalar product)B = 22.0m^2
    B(dot/scalar product)C = 39.0m^2

    Find magnitude of A and its direction (angle)?


    2. Relevant equations
    Bx = Bcosθ
    By = Bsinθ
    Trig


    3. The attempt at a solution
    For Q1 I have tried a variety of methods. To obtain a few angles or magnitudes but I am literally stuck, not even sure where to start. I tried to find the angle between B and C to obtain the Magnitude of C which will equal A... afterwards find the angle between A and B with the newly found magnitude (A = C). Maybe that is the wrong approach, but I could not figure out how to find Mag of C without Cx or Cy...

    I am not sure how else to transcribe the math I have on paper to this forum, but if this is lacking information a hint in the right direction would be truly appreciated.

    Thanks a lot,
    Cd
     
    Last edited: May 30, 2012
  2. jcsd
  3. May 30, 2012 #2
    As a hint, one definition of dot product is: $$ A \cdot B=\left\|A\right\| \, \left\|B\right\| \cos \theta $$, where ##\theta## is the angle between the two vectors. I would look for ##\theta## first.
     
  4. Jun 1, 2012 #3
    Like Joffan said, for vectors a andb, ##\mathfrak R\left(\vec a\cdot\vec b\right)=\left\|a\right\| \, \left\|b\right\| \cos \theta##
     
    Last edited: Jun 1, 2012
  5. Jun 1, 2012 #4

    SammyS

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    Hello cdphys. Welcome to PF !
     
    Last edited: Jun 1, 2012
  6. Jun 1, 2012 #5
    Oops! I edited my post!
     
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