The magnitude of the vertical force $\mathbf{W}$ is $160 \mathrm{~N}$. The direction cosines of the position vector from $A$ to $B$ are $\cos \theta_x=0.500$, $\cos \theta_y=0.866$, and $\cos \theta_z=0$, and the direction cosines of the position vector from $B$ to $C$ are $\cos \theta_x=0.707, \cos \theta_y=0.619$, and $\cos \theta_z=-0.342$. Point $G$ is the midpoint of the line from $B$ to $C$. Determine the vector $\mathbf{r}_{A G} \times \mathbf{W}$, where $\mathbf{r}_{A G}$ is the position vector from $A$ to $G$.
(FIGURE CAN'T COPY)