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Homework Help: Finding Length of a Vector

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the length of the vector C starting from the components given in Equations 3 and 4.
    Express C in terms of A, B, and theta.


    2. Relevant equations
    3. Cx= A + Bcos([tex]\theta[/tex]),
    4. Cy = Bsin([tex]\theta[/tex]).


    3. The attempt at a solution
    C = [tex]\sqrt{C_x ^2+C_y ^2}[/tex]
    C = [tex]\sqrt{A^2+(Bcos\theta)^2+(Bsin\theta)^2}[/tex]
    using trig identity cos2 [tex]\theta[/tex]+sin2 [tex]\theta[/tex]=1
    C = [tex]\sqrt{A^2+2B^2}[/tex] ???
     
  2. jcsd
  3. Aug 31, 2010 #2

    CompuChip

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    You have all the right ingredients, but be careful!

    [tex](A + B \cos\theta)^2[/tex] is not the same as [tex]A^2 + (B \cos\theta)^2[/tex].

    This is a classical trap... (x + 1)² is not equal to x² + 1²... to see what it does equal, you can write it out as (x + 1)(x + 1) and expand the brackets.
     
  4. Aug 31, 2010 #3
    C = [tex]\sqrt{A^2 + 2ABcos\theta + B^2}[/tex]
     
  5. Aug 31, 2010 #4

    CompuChip

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    Now you're just sloppy and maybe guessing a bit, aren't you? :)
    Please work it out carefully and you'll get the right answer.
     
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