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Math Help - Parallelogram

  1. #1
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    Parallelogram

    (1) Prove that the diagonals of an equilateral parallelogram are perpendicular.

    So this is basically a square right? Is this essentially the same thing as  (A-B) \cdot (A+B) = 0 where both of these vectors give the diagonals?

    (2) Prove the law of sines using the cross product.

    So we want to prove that  \frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}

    So  A \times B = |A||B| \sin \theta gives the area of a parallelogram formed by  A,B,C . How would I proceed from here?
    Last edited by shilz222; November 26th 2007 at 02:05 PM.
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  2. #2
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    (1) Realize that if A & B are vectors that are adjacent sides of a parallelogram then (A+B) and (A-B) are the diagonals. We know \left( {A + B} \right) \cdot \left( {A - B} \right) = \left\| A \right\|^2  - \left\| B \right\|^2. Recalling what equilateral means the result follows at once.
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