Consider the support arm for a lifting mechanism shown below. The weight of the setup is $100$ N and acts at the center of gravity which is at location E; point E is $0\mathrm{.}5$ m from the x$-$axis in the X $-$Y plane as shown below. The arm supports a load at point D of T$=(1000$i$-1000$k$).$ Note that the distance between points A and C is $1$ m$.$ Point C shown in the diagram below is a bearing that supports radial load only. Point A is a ball and socket, while Point B is a roller. Do the following:

$1)$ Calculate the forces in vector form at the three supports A$,$ B$,$ and C$.$

$2)$ Calculate the magnitude of the forces at each support.