Problem #$6(10$ Points$)$

Determine the greatest force $F$ that can be applied to the ring at $A$ if each cable can support a maximum force of $500$ lb $.$

$r_{AB}=3i-2j-6k$&$u_{AB}=\mathrm{.}43i-\mathrm{.}29j-\mathrm{.}86k$

$r_{AC}=-3i-6k$&$u_{AC}=-\mathrm{.}45i-\mathrm{.}9k$

$r_{AD}=3j-6k$&$u_{AD}=\mathrm{.}45j-\mathrm{.}9k$