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Math Help - Area of a Parallelogram with Vertices..

  1. #1
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    Area of a Parallelogram with Vertices..

    [1,2,3]
    [1,3,6]
    [3,8,6]
    [3,7,3]

    I know I have to find 2 (I think) vectors that determine the area and then I take the cross product of the 2. That's about all I know I don't know which 2 determine the area.
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  2. #2
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    Quote Originally Posted by sfgiants13 View Post
    [1,2,3]
    [1,3,6]
    [3,8,6]
    [3,7,3]

    I know I have to find 2 (I think) vectors that determine the area and then I take the cross product of the 2. That's about all I know I don't know which 2 determine the area.
    The given vectors are the stationary vectors of the vertices of the parallelogram. Calculate the vectors describing the sides of the parallelogram:

    \overrightarrow{AD} = \vec d - \vec a = [2,5,0]

    \overrightarrow{BC} = \vec c - \vec b = [2,5,0]
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    \overrightarrow{AB} = \vec b - \vec a = [0,1,3]

    \overrightarrow{DC} = \vec c - \vec d = [0,1,3]
    - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

    You now know the pairs of parallels. As you have written, the area is

    a_{parallelogram} = |\overrightarrow{AD} \times \overrightarrow{AB}| =| [2,5,0] \times[0,1,3] |= | [15,-6,2] | = \sqrt{265} \approx 16.2788
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