(Solved): Given \( F=408 N \) and the dimensions below, find the unit vector and force magnitude for each cab ...

Given \( F=408 N \) and the dimensions below, find the unit vector and force magnitude for each cable. Note that \( \mathrm{B}, \mathrm{C} \), and \( \mathrm{D} \) are in the \( x y \) plane, and \( \mathrm{A} \) is on the \( z \) axis. a) Find the unit vector for each cable. \( \begin{array}{llll}\mathbf{u}_{A B}= & \mathbf{i}+ & \mathbf{j}+ & \mathbf{k} \\ \mathbf{u}_{A C}= & \mathbf{i}+ & \mathbf{j}+ & \mathbf{k} \\ \mathbf{u}_{A D}= & \mathbf{i}+ & \mathbf{j}+ & \mathbf{k}\end{array} \) b) If the system is in static equilibrium, find the magnitude of force in each cable. \( \begin{array}{ll}F_{A B}: & \mathrm{N} \\ F_{A C}: & \mathrm{N} \\ F_{A D}: & \mathrm{N}\end{array} \)