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I Show that the diagonals are perpendicular using vectors

  1. Aug 28, 2016 #1
    I am given the following problem: Show, using vectors, that the diagonals of an equilateral parallelogram are perpendicular.

    First, imagine that the sides of the equilateral parallelogram are the two vectors ##\vec{A}## and ##\vec{B}##. Since the figure is equilateral, their magnitudes must be equal: ##A = B##. Then ##A^2 - B^2 = 0##. This can be factored using the dot product as ##(\vec{A} + \vec{B}) \cdot (\vec{A} - \vec{B}) = 0##. However, these two vectors are the diagonals of the parallelogram, and since their dot product is zero, they must be perpendicular.

    Is this proof sufficient? Is there a better proof?
     
  2. jcsd
  3. Aug 28, 2016 #2

    blue_leaf77

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    Science Advisor
    Homework Helper

    I would go with your proof.
     
  4. Aug 29, 2016 #3

    Mark44

    Staff: Mentor

    You should be posting this and your other homework-type problems in the Homework & Coursework sections.
     
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