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Math Help - 2-forms

  1. #1
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    2-forms

    Find the value of the 2-form  dx \ dy + 3dx \ dz on the oriented triangle with vertices  (0,0,0), \ (1,2,3), \ (1,4,0) .

    I drew the projection of the triangle on each of the coordinate planes. Now what do I do? Do I compute the area of the triangle on the  xy plane?

    Because  \text{flow} = A dy \ dx + B dz \ dx + C dx \ dy
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  2. #2
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    Is the basically the sum of the areas in the projected planes?
    Last edited by shilz222; November 10th 2007 at 12:33 PM.
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  3. #3
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    The answer is  -3 \frac{1}{2} . And if it is a 2 form then it has to be assigned a number to a oriented surface. Maybe I should draw a prism?
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  4. #4
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    I think I got it. Its  \left(\text{area of projection on xy axis} \right) + \left( 3 \times \text{area of projection on xz  axis} \right) .

    I ended up getting  - \left( \frac{18}{4} - \frac{\sqrt{14}}{4} \right) \approx -3.5
    Last edited by shilz222; November 10th 2007 at 01:50 PM.
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  5. #5
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    But if the surface is not a triangle then you can't do this right?
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