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Volume of a parallelepiped

  1. Nov 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that the volume of a parallelepiped with edges [tex] A,B,C [/tex] is given by [tex] A \cdot (B \times C) [/tex].

    2. Relevant equations



    3. The attempt at a solution

    [tex] B \times C [/tex] is the area of a parallelogram. From here I would I deduce the above result?
     
  2. jcsd
  3. Nov 26, 2007 #2
    Is [tex] A [/tex] just the height?
     
  4. Nov 26, 2007 #3
    You're right, in two dimensions x and y the area is A=|bxc|. The height is actually |a|*|cos(theta)|. Where theta is the angle between vector a, and the cross product of vectors b and c. I'll include a picture but I hope this helps analytically to prove it. V=|a dot product to (b cross product with c.
     
  5. Nov 26, 2007 #4

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