Cable $AB$ exerts a $200lb$ magnitude force vec$(F{)}_{AB}$ and cable $AC$ exerts force vec$(F{)}_{AC}=-166$hat$(i)+50$hat$(j)+100$hat$(k)$ lb both at point $A$ in the system shown.

Answer the following showing all steps of your work:

A$)$ Express vec$(F{)}_{AB}$ in terms of components.

B$)$ Determine the magnitude of the resultant force.

C$)$ Determine the three direction angle of the resultant force.

Enter the value you got for B$)$ in the window below. Work will be graded based on your detailed written work for all parts.