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Adding Vectors homework

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data

    If B is added to C = 3.0î + 4.0ĵ, the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C. What is the magnitude of B?

    2. Relevant equations

    a = sqrt(ax2 + ay2)

    3. The attempt at a solution

    1. Found the magnitude of C

    c = sqrt(cx2 + cy2) = sqrt(32 + 42) = 5

    2. Added B to C and got this equation

    5 = sqrt(ax2 + ay2) = sqrt(b2 + 52)

    which obviously isn't right because I get the magnitude of B as 0. I'm not sure what I am doing wrong, but any guidance would be helpful. Thank you.
  2. jcsd
  3. Sep 12, 2009 #2
    Think it through.

    The equation you are trying to solve is;


    In words "the magnitude of B plus the magnitude of C equals the magnitude of C"

    You don't even need to find their magnitudes.

    Make sense yet?

  4. Sep 12, 2009 #3
    If B + C = result R, then B = R - C. Convert the phrase "the result is a vector in the positive direction of the y axis, with a magnitude equal to that of C" into a components and a unit vector, and then subtract C from it, vector arithmetic. They're asking you for the magnitude of that last one.
  5. Sep 12, 2009 #4
    That's not what the question says.
  6. Sep 12, 2009 #5
    "That's not what the question says."

    No, I don't agree.

  7. Sep 12, 2009 #6
    C and "the result" R have the same magnitudes, and yet C has two positive components, while R is entirely in the +y direction. What are you gonna add to C to get R? Hint: Its magnitude will be an irrational number that has to be rounded off according to the number of significant digits in the given components of C.
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