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Homework Help: Find components of vector C from vectors A and B

  1. Jan 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Given vectors [tex]\vec{A} = 5.0\hat{i} - 6.5\hat{j}[/tex] and [tex]\vec{B} = -3.5\hat{i}= 7.0\hat{j}[/tex]. Vector [tex]\vec{C}[/tex] lies in the xy-plane. Vector [tex]\vec{C}[/tex] is perpendicular to [tex]\vec{A}[/tex] and the scalar product of [tex]\vec{C}[/tex] with [tex]\vec{B}[/tex] is 15.0. Find the vector components of [tex]\vec{C}[/tex].

    2. Relevant equations

    [tex]\vec{A}{\cdot}\vec{C} = 0 [/tex]
    [tex]\vec{B}{\cdot}\vec{C} = 15 [/tex]

    [tex]\vec{B}{\cdot}\vec{C}=B_{i}C_{i}+B_{j}C_{j}=15 [/tex]
    [tex]\vec{B}{\cdot}\vec{C}=-3.5C_{i}+7.0C_{j}=15[/tex]

    [tex]\vec{A}{\cdot}\vec{C}=A_{i}C_{i}+A_{j}C_{j}=0[/tex]


    3. The attempt at a solution

    Since the vectors A and C are perpendicular
    [tex]\vec{A}{\cdot}\vec{C} = 0 [/tex]
    Then,
    [tex]\vec{A}{\cdot}\vec{C}=A_{i}C_{i}+A_{j}C_{j}=0[/tex]
    [tex]\vec{A}{\cdot}\vec{C}=5.0_{i}C_{i}-6.5_{j}C_{j}=0[/tex]
    [tex]C_{j}=\frac{5.0_{i}C{i}}{6.5}[/tex]

    Plug in [tex]C_{j}[/tex] into the other scalar equation and solve for [tex]C_{i}[/tex]. Basic substitution. However I keep getting the wrong answer. Am I approaching the problem incorrectly or is my algebra wrong?

    The correct answer is [tex]C_{x} = 8.0[/tex] and [tex]C_{y} = 6.1[/tex]
     
    Last edited: Jan 20, 2010
  2. jcsd
  3. Jan 20, 2010 #2

    rl.bhat

    User Avatar
    Homework Helper

    Hi casemeister06, welcome to PF.
    -3.5Ci + 7Cj = 15.......(1)
    5.0Ci - 6.5Cj = 0.........(2)
    Multiply by 0.7 to eq. (2) and add it to eq.(1) and solve for Cj.
     
  4. Jan 21, 2010 #3
    Yeah, I don't know what I was doing, but I got it right now. I think I was messing up on my algebra or something. Thanks for the help.
     
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