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
    |(b-a)x(d-a)|
    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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