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Vector Proofs using vector components

  1. Sep 11, 2003 #1
    Hi! I'm new to the forums. I'm taking an introduction to physics class this semester and I've been having some difficulty with it. Oh, I also wanted to let you know that it's been a while since I've taken calculus or any other math class for that matter. But I need physics to graduate. Anywho ... the question that I have deals with vector components.

    Two vectors of magnitudes a and b make an angle theta (which I'll represent as @) with each other when placed tail to tail. Prove, by taking components along two perpendicular anes, that

    r = the square root of (a^2 + b^2 + 2abcos@)

    gives the magnitude of the sum vector R (vector R = r with that arrow above it) of the two vectors.

    Well this is what I have so far:

    vector A = Axi + Ayi
    vector B = Bxi + Byi
    vector R = vector A + vector B

    A^2 = Ax^2 + Ay^2
    B^2 = Bx^2 + By^2
    R^2 = A^2 + B^2

    A dot B = A*B = ABcos@

    I can see how r = square root of (A^2 + B^2) but where does the 2ABcos@ come in. I have a feeling that it deals with the A*B product, but I don't know how to fit it in.
     
  2. jcsd
  3. Sep 11, 2003 #2
    A dot A=a^2 (a is magn A) A- vector
    B dot B=b^2 -the same-
    =>
    (A+B) dot (A+B)=a^2+b^2+2*A dot B=r^2 (evidently)
    ...so r^2 =a^2+b^2+2*a*b*cos@...
    ...do you really have to use components ???
     
  4. Sep 11, 2003 #3
    well, the problem said to use components .. so i believe so.

    thanks for your help!
     
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