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Vector and its components

  1. Jan 21, 2010 #1
    1. The problem statement, all variables and given/known data
    force vector F = 700[-0.25, 0.433, 0.866].
    vector A = [-4, 4, 2]
    a)What is the component of F that is parallel to A?
    b}And what is component of F that is perpendicular to A?

    2. Relevant equations
    [tex]A\bullet F = |A||F|\cos{\theta}[/tex]
    When two vectors are parallel:
    [tex]A\bullet B = |A||B|| [/tex]
    When two vectors are perpendicular
    [tex]A\bullet B = 0 [/tex]


    3. The attempt at a solution
    I'm not sure if I should use the dot product to find the component but I figure that would be the simplest way to do so.
    A = [-4, 4 ,2] = 6[-2/3, 2/3, 1/3]
    The parallel force vector = s[-2/3, 2/3, 1/3]
    That's all I have right now. If I use the dot product equation, both sides of the equation will come to the same term and cancel each other out. I think my definition for the parallel force vector is too general as s could be any scalar.
     
  2. jcsd
  3. Jan 22, 2010 #2
    Note that
    [tex]
    F_{parallel} = |F|\cos{\theta}
    [/tex]
    (this is obvious if you draw two vectors on paper and apply a little trig)

    So
    [tex]
    A\bullet F = |A|F_{parallel}
    [/tex]
    Then just use the definition of the dot product to calculate the left hand side and solve for the parallel component
     
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