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Volume of parallelepiped(Linear Algebra)

  1. Mar 27, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the volume of a parallelepiped having u,v, and w as adjacent sides is given by abs(u*(vXw)).

    (The star means dot product)

    I am not really sure how to solve this problem. I was thinking that Volume would equal norm(u)+norm(v)+norm(w), but I couldn't figure out anywhere to go from there. Can someone help me start this problem. Thanks.
     
  2. jcsd
  3. Mar 27, 2009 #2

    djeitnstine

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    Gold Member

    First you should realize the dot product of 2 vectors is also the area of a parallelogram. Then you should note that the height of the parallelepiped is the projection of the vertical line to the line orthagonal (this should give you a hint) of the 2 vectors.
     
  4. Mar 30, 2009 #3
    Awesome, thanks
     
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