I am given the following problem: Show, using vectors, that the diagonals of an equilateral parallelogram are perpendicular.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# I Show that the diagonals are perpendicular using vectors

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