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Adding Vectors

  1. Jan 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Just a quick question. In the attached image, I can say [itex]\vec{am}=\vec{c}-\frac{1}{2}\vec{a}[/itex]. Although subtraction is not commutative, can I also say (relative strictly to vectors) that [itex]\vec{am}=-\frac{1}{2}\vec{a}+\vec{c}[/itex], considering [itex]\vec{am}=\frac{1}{2}\vec{ao}+\vec{c}[/itex]?

    Many thanks.
     

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  3. Jan 13, 2013 #2

    Mark44

    Staff: Mentor

    Subtraction isn't commutative, as you noted, but addition is, and that's really what you're doing. a - b = a + (-b), which is the same as -b + a.
     
  4. Jan 13, 2013 #3

    SammyS

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    Saying that [itex]\ \vec{am}=\vec{c}-\frac{1}{2}\vec{a}\ [/itex] is essentially the same as saying [itex]\ \vec{am}=-\frac{1}{2}\vec{a}+\vec{c}\,,\ [/itex] because [itex]\ \vec{c}-\frac{1}{2}\vec{a}=\vec{c}+ \left(-\frac{1}{2}\vec{a}\right)\ [/itex] and vector addition is commutative.
     
  5. Jan 13, 2013 #4
    Great. Thank you very much.
     
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