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Integral of an exponential divided by a root function

  1. Jan 26, 2008 #1
    1. The problem statement, all variables and given/known data

    Prove that the diagonals of a parallelogram bisect each other.

    2. Relevant equations

    I chose one vertex as the origin, one as a and one as b. The final vertex was a+b.

    3. The attempt at a solution

    The diagonals were [tex]\vec{r_1}=\vec{a}+\vec{b}[/tex] and [tex]\vec{r_2}=\vec{b}-\vec{a}[/tex]. Where do I go from here? Can I assume that they go through the center of the parallelogram or do I have to prove that too?
  2. jcsd
  3. Jan 26, 2008 #2


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    What is the definition of a vertex?
  4. Jan 26, 2008 #3
    Err... a point where two vectors intersect?
  5. Jan 27, 2008 #4


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    Your vectors "begin" at one vertex, right? What vector, starting at that vertex, has its "end" at the midpoint of [itex]\vec{a}+ \vec{b}[/itex]? [itex]\vec{b}-\vec{a}[/itex]?
    (Note that, since [itex]\vec{b}-\vec{a}[/itex] "starts" at [itex]\vec{a}[/itex] instead of the origin, the midpoint of [itex]\vec{b}-\vec{a}[/itex] is at [itex]\vec{a}[/itex] plus half of [itex]\vec{b}-\vec{a}[/itex].)
    Last edited by a moderator: Jan 28, 2008
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