$($c$)($i$)$ For the structure shown in Figure $5\mathrm{.}3,$ determine the moment of the force $F$ acting at $B$ about the axis extending between A and $C.$ The magnitude of the force is $|F|=130N$ and it is acting along the direction of the vector $4i+12j+3k.$ Assume the point $A$ is at the origin of the coordinate system.

$[10$ marks$]$

$($ii$)$ Express the moment as a Cartesian vector.

$[2$ marks$]$

Figure $5\mathrm{.}3$