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Cross Product - Vertices

  1. Apr 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Let A = (-5, -2, -5), B = (-7, -7, -6), C = (-3, -3, 0), and D = (-5, -8, -1). Find the area of the parallelogram determined by these four points.


    2. Relevant equations
    Area of Parallelogram = ||a x b||

    3. The attempt at a solution
    I drew the parallelogram and decided to use CA and CD as my two vectors for the cross product. Finding the vector for each came from the following:

    CA = C - A = <-3, -3, 0> - <-5, -2, -5> = <2, -1, 5>
    CD = C - D = <-3, -3, 0> - <-5, -8, -1> = <-2, -5, -1>

    Then I took the cross product:

    CA x CD = <26, -8, -12>

    To which I tried to find the magnitude:
    ||CA x CD|| = √( 26^2 + (-8)^2 + (-12)^2) = √995

    I submitted this to Webwork but it says this answer is wrong; can someone explain to me what went wrong?
     
  2. jcsd
  3. Apr 7, 2012 #2

    SammyS

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    Your cross product is correct.

    Check your arithmetic on 262 + (-8)2 + (-12)2 .
     
  4. Apr 7, 2012 #3

    LCKurtz

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    Everything looks good except the last ##\sqrt{995}##.

    [Edit]: Good timing Sammys.
     
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