Well... here's what I got so far:
I pretty much focused on OA... I did normalize the vector equation to get
[2/sqrt(21)] i + [1/sqrt(21)] j + [4/sqrt(21] k *This is after simplification, the magnitude of OA is 5sqrt(21)*
Realizing this will create ratios of force, and that the magnitude of the normal equation is 1, I then put this through the
projection formula:
proj
v u = (u.v/||v||^2)v
Letting u = OA and v = the 1000kg vector... the x and y components logically no longer matter and its projection comes out to be
(4sqrt(21))/21 k
Then finding the magnitude of that projection resulted in:
16/21
And that is how the cookie crumbled for me... does that seem right???
I do like to learn different routes of logic, and vector math in calc 3 has definitely introduced me to that... so I really do appreciate the hints and everything. Helps me out a lot.
_joe
Update: thinking about it... the 16/21 had to be its portion of the load... so the actual load bearing capacity i came up with was ~762... but i still dont know if its right...