Finding Force vector

1. Dec 2, 2005

DOMINGO79

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!

2. Dec 2, 2005

amcavoy

Write out the cross product as a determinant with the force vector's components a,b,c. Then you can solve:

$$\det{\begin{bmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k} \\ 3&4&5 \\ a&b&c\end{bmatrix}}=16\mathbf{i}-20\mathbf{j}-5\mathbf{k}$$

3. Dec 3, 2005

DOMINGO79

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?

4. Dec 3, 2005

Tide

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.

5. Dec 4, 2005

DOMINGO79

Wow....

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

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

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