Problem $3$:

The balloon shown below exerts a $1600$ N force $F$ on the hook at $O.$ The vertical line $AB$

intersects the $x-z$ plane at point A $.$ The angle between the z axis and the line OA is $60,$

and the angle between the line OA and $F$ is $60.$

Express $F$ in terms of Cartesian components;

Determine the direction cosines of $F$;

Find the unit vector of $F$ in terms of Cartesian components.