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Physics formula for vectors

  1. Sep 12, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the area of the parallelogram with the vectices :

    A(-2,1)
    B(0,4)
    C(4,2)
    D(-2,1)

    2. Relevant equations

    This sections is about vectors, specifically crossproducts.

    A = |a|(|b|sin(/theta) = |a x b|

    - The length of the cross product a x b is equal to the area of the parallelogram determined
    by a and b



    3. The attempt at a solution

    Instead of using the equation i found the length of each line :

    A to B = sqrt(13)
    B to C = sqrt(20)
    D to C = sqrt(14)
    A to D = sqrt(20)

    What I did was divide it into 2 triangles find each hypotenuse and multiply it by each other
    then divide it by 2. I don't know if there is a formula similar to this but the answer I got
    was 16.748.

    The problem I am having is to use the definition in the Relevant equation sections above.
    How do I know which points would be a vector. If I know that then I can
    probably figure about there Cross product and find its magnitude which is the parallelogram area.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 12, 2009 #2
  4. Sep 12, 2009 #3
    Re: Vectors

    Oh I see, All I need is x and y : x*y = Area, where x & y are vectors.

    But will it always be the case that the length of the A to D will be equal to the length B to C?
     
  5. Sep 12, 2009 #4
    Re: Vectors

    Remember to take the magnitude of the cross product (i.e |x*y| )

    No.
     
  6. Sep 12, 2009 #5
    Re: Vectors

    How do I counteract that if it does not have the same length on the opposite side.

    Do I have to do 2 cross product?
     
  7. Sep 12, 2009 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Vectors

    Opposite sides in a parallelogram are always of equal length.
     
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