1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.

  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook