A $450-$lb load hangs from the corner C of a

rigid piece of pipe ABCD that has been bent

as shown. The pipe is supported by ball$-$and$-$

socket joints A and D$,$ which are fastened, re$-$

spectively, to the floor and to a vertical wall,

and by a cable attached at the midpoint E of

the portion BC of the pipe and at a point G on

the wall. Determine $($ a $)$ where G should be lo$-$

cated if the tension in the cable is to be min$-$

imum, $($b$)$ the corresponding minimum value

of the tension. Show details of coordinates of points A$,$ B$,$ C$,$ and D and E$,$ and the detailed computations of the directional vectors AC$,$ AD$,$ AE$,$ and the unit vector $.$