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Area of a parallelogram using determinants

  1. Feb 16, 2009 #1
    1. The problem statement, all variables and given/known data

    let v = (1,0,1) and u = (0,2,1)

    Find the area of the parallelogram {sv + tu : 0 <= s, t <=1)

    2. Relevant equations



    3. The attempt at a solution

    I know the area of a parallelogram is the determinant of a 2x2 matrix, but they gave v and u in R^3. Would I just ignore the z component in this case?
     
  2. jcsd
  3. Feb 16, 2009 #2
    technically there is a 3rd vector which could be r = (0,0,0)

    and NEVER ignore any component given in a question like this :P

    So, let the origin = r therefore find the vectors rv and ru
    Then, find the magnitude of the cross product of the two vectors, rv and ru
    i.e. |rv x ru|
    Your answer should be the Area of the Parallelogram. The Area of a Triangle formed in vectors is HALF the Parallelogram.

    I hope i've been helpful.

    missbooty87
     
  4. Feb 16, 2009 #3
    I could be wrong but isnt (0,0,0)(1,0,1) = 0?
     
  5. Feb 16, 2009 #4
    yes..... But how is that relevant to your question... i said find the two new vectors and then cross multiply the two new vectors he he... not multiply or cross-multiply the individual vectors he he...

    And if I wasn't clear let me rephrase.
    --------------------
    1st step:

    find the two new vectors

    the first vector is from R to V (i.e. From the Origin to the vector v)
    the second vector is from R to U
    --------------------
    2nd step:

    Cross multiply the RV and RU (i.e. |RV x RU|)
    --------------------
    3rd step:

    Claim that you have the answer
    --------------------

    If you don't understand let me know.
     
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