Problem $2\mathrm{.}126$ The two segments of the L$-$shaped bar

are parallel to the $x$ and $z$ axes. The rope $AB$ exerts

a force of magnitude $|F|=500lb$ on the bar at $A.$

Determine the cross product $r_{CA}F,$ where $r_{CA}$ is the

position vector form point $C$ to point $A.$

Problem $2\mathrm{.}164$ The magnitude of the vertical force $W$

is $160$ N $.$ The direction cosines of the position vector from

$A$ to $B$ are $cos{}_x=0\mathrm{.}500,cos{}_y=0\mathrm{.}866,$ and $cos{}_z=$

$0,$ and the direction cosines of the position vector from

$B$ to $C$ are $cos{}_x=0\mathrm{.}707,cos{}_y=0\mathrm{.}619,$ and $cos{}_z=$

$-0\mathrm{.}342.$ Point $G$ is the midpoint of the line from $B$ to $C.$

Determine the vector $r_{AG}W,$ where $r_{AG}$ is the position

vector from $A$ to $G.$