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College Math

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show that the quadrilateral with vertices at the following points is a parallelogram and find its area. a = (5,2,0), b = (2,6,1), c = (2,4,7), d = (5,0,6)

  • College Math -

    AB has direction (-3,4,1)
    BC has direction (0,-2,6)
    CD has direction (3,-4,-1)
    DA has direction (0,-2,6)

    So, AB || CD
    and BC || AD

    since the sides are parallel in pairs, they must have the same lengths in pairs (I trust you can verify this).

    the area is just
    where a,b,c,d are the vectors to the points A,B,C,D.

  • College Math -

    thanks steve. u really help me out.. really appreciate it .. =)

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