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Relying on my past knowledge on how to attack the problem, I should use the equation Moment of B about AC = $r_{AB} \times B • n^ AC$ To find the least force on B.

I just don't know what position vector I should use for B, I am certain that I should not use points A OR C as a reference to get its position vector. That's what I believe. Or should I use it? Or the way I know is not the right way of solving? Is there any other way?

Sharing what I've done so far, I tried solving the midpoint of line AC, thinking force B could be from point B to the midpoint of line AC. Say, I've got my position vector for force B, I continued solving for $r×B$, then the dot product of the answer and unit vector AC, and I've got force B as 28 lb., and since my process is unclear surely my answer was wrong, too.

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You need to compute the length of the moment arm from $B$ to $\overline{AC}$

That is the height of the triangle, and can be computed directly from tuples as $\frac{\|\overline{AC} \times \overline{AB} \|}{\|\overline{AC}\|}$

So $\overline{AC}\times\overline{AB}= \{72,108,54\}\qquad\|\overline{AC}\times\overline{AB}\|= 140.58\,sqin$

and $\overline{AC}=\{-9,6,0\}\qquad\|\overline{AC}\|=10.82\,in$

$140.58\, sqin/10.82\,in=13\,in$

$260\, in\, lbf/13\, in = 20\, lbf$

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  • $\begingroup$ Turned out I should just use the definition of moments and not the other way I thought. Really appreciate how you pointed it out. Now I know this problem should be an easy one $\endgroup$ – keplerxx Jan 25 at 8:54

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