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Vectors Overthought?

  1. Jun 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Given:
    A (-3,7)
    B (5,22)
    C (8,18)
    are 3 points in 2D space.

    Find [itex]|\vec{AB} + \vec{BC}|[/tex]

    2. Relevant equations
    [tex]||\vec{v} - \vec{w}||^2 = ||\vec{v}||^2 + ||\vec{w}||^2 - 2 ||\vec{v}|| \cdot ||\vec{w}|| \cos \theta[/tex]


    3. The attempt at a solution
    Isn't [itex]|\vec{AB} + \vec{BC}|[/tex] just [itex]|\vec{AB}| + |\vec{BC}|[/tex]? I mean, isn't the magnitude of the sum of 2 vectors the same as adding the 2 magnitudes together?
     
  2. jcsd
  3. Jun 18, 2009 #2
    Draw it out and see :smile:
     
  4. Jun 18, 2009 #3
    I tried. What I'm confused about is the interpretation of [itex]|\vec{AB} + \vec{BC}|[/tex]

    I mean, mathematically, I believe I can do this:
    [itex]|\vec{AB} + \vec{BC}|[/tex] = [itex]|\vec{AC}|[/tex]
    Because [itex]\vec{AB} + \vec{BC}[/tex] = [itex]\vec{AC}[/tex]

    In which case, [itex]|\vec{AB} + \vec{BC}|[/tex] is intuitive.
    But I might be getting myself confused

    Lastly, my teacher insisted that the cosine law be used, and I have no idea why.
     
  5. Jun 18, 2009 #4

    Pengwuino

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    Gold Member

    Edit: Disregard this post
     
    Last edited: Jun 18, 2009
  6. Jun 18, 2009 #5
    So are you saying [itex]|\vec{AB} + \vec{BC}|[/tex] = [itex]|\vec{AC}|[/tex]?

    If so, why does my teacher insist that I use the cosine law?
     
  7. Jun 18, 2009 #6

    Pengwuino

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    Gold Member

    Oh wait wait, my bad, I didn't read those vectors correctly. Disregard my first post.

    Yes, the magnitude of (AB + BC) is equal to the magnitude of AC because the vector AC is the same as the vector you get from adding AB and BC thus it has the same magnitude.
     
  8. Jun 18, 2009 #7
    I still don't understand why I would need to use cosine law for this, as claimed by my teacher...
     
  9. Jun 18, 2009 #8

    Pengwuino

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    Gold Member

    Unless I'm not seeing something, I don't see the need for it. Are you sure you aren't looking for |AC + BC|?
     
  10. Jun 19, 2009 #9
    No but ][itex]|\vec{AB} + \vec{BC}|[/tex] and [itex]|\vec{AB}| + |\vec{BC}|[/tex] are related. Question: how?
     
  11. Jun 19, 2009 #10
    [itex]
    \vec{AB} + \vec{BC}= \vec{CA}
    [/itex]

    So, you need to find [itex]|\vec{-AC}|=|\vec{AC}|[/itex]

    Regards.
     
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