$22$ in $.$ vertical rod $\backslash ($ C D $\backslash )$ is welded to the midpoint $\backslash ($ C $\backslash )$ of the $50-$in$.$ rod $\backslash ($ A B $\backslash ).$ Determine the moment about $\backslash ($ A B $\backslash )$ of the $\backslash (250-1$ b $\backslash )$ force $\backslash ($ Q $\backslash )$ by the method indicated. Given a $\backslash (=18\backslash$mathrm$\{$in$\}\backslash ).$

Using moment of force Q applied at point D about point B $.$

$\backslash ($ y $\backslash )-$component of point $\backslash ($ D$=\backslash )$ in$.$

Unit vector from D to $\backslash (\backslash$mathrm$\{$H$\}=\backslash )$

I $+$

Force $\backslash ($ Q$=\backslash )$

lb$.1+$

lb$.$j $+$

lb$.$ k

Position vector from $\backslash ($ B $\backslash )$ to $\backslash ($ H$=\backslash )$

in$.$ I $+$

in$.$ J $+$

in$.\backslash (\backslash$mathbf$\{$k$\}\backslash )$

Moment about point $\backslash ($ B$=\backslash )$

lb in$.$ I $+$

lb in$.$ J $+$

lb in$.$ k

Unit vector from A to $\backslash (\backslash$mathrm$\{$B$\}=\backslash )$

$\backslash (1+\backslash )$

J $+$

k

Moment about AB of the $250$ lb force Q

lb in$.$