Least force required

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.

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

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

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

• 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 – keplerxx Jan 25 at 8:54