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Finding Force vector

  1. Dec 2, 2005 #1
    I am having a huge problem trying to answer the following question:
    Given the position vector r = 3i + 4j + 5k and torque = 16i - 20j - 5k, find the force vector F which will give the correct result, so that torque = r x F
    Can anyone please help me solve this!:confused:
     
  2. jcsd
  3. Dec 2, 2005 #2
    Write out the cross product as a determinant with the force vector's components a,b,c. Then you can solve:

    [tex]\det{\begin{bmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k} \\ 3&4&5 \\ a&b&c\end{bmatrix}}=16\mathbf{i}-20\mathbf{j}-5\mathbf{k}[/tex]
     
  4. Dec 3, 2005 #3
    16i-20j-5k = i j k = i(4c-5b)-j(3c-5a)+k(3b-4a)
    3 4 5
    a b c

    16i = i(4c-5b) -3(16 = 4c-5b) -48 = -12c + 15b
    -20j = -j(3c-5a) → 4(20 = 3c-5a) → 80 = 12c – 20a
    -5k = k(3b-4a) 32 = 15b -20a

    32 = 15b-20a 32 = 15b-20a
    5(-5 = 3b-4a) → -25 = -15b+20a, so what am I doing wrom?

    why are the unknowns totally canceling out?
     
  5. Dec 3, 2005 #4

    Tide

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    They don't cancel out. You're not expanding the determinant correctly.

    For example, your first equation should read: 16 = 4c - 5b and nothing else.
     
  6. Dec 4, 2005 #5
    Wow....

    Hey, thanks alot, I think I just opened my eyes:bugeye: and understand how to complete the question...

    If I have anymore Q's, I will let you know, thanks...
     
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