Show all calculations and steps clearly.

Problem $1($Figure A$).,B(-1,2,2)$

$($a$)$ Express the force $F$ in vector form.

$($b$)$ Calculate the moment of the force $F$ about the point $O.$

Problem $2($Figure A$).$

Calculate the moment of the force $F$ about the axis joining the points $O$ and $C.$

Problem $3($Figure B$).$

Calculate the forces in the cables $AB$ and $AC.$ The weight of the block is $550lb$ and the point $A$ is in static equilibrium. Draw the free$-$body diagram of the point $A.$

Problem $4($Figure C$).$

Replace the force system with a resultant force and moment at $O.$

Figure A

Figure B