Statics: Equilibrium in 3-Dimensions, Part II

This is the problem we solved back in the previous lecture.

Here's the diagram:

Now we have to draw the free body diagram. The rules that you have to remember are encircled: 

We're looking for the magnitude, and we can use the unit vector going into the same direction. Remember moment is Force x length. 

and we get the following equation, solving for Fb and Fc in the same way in regards to momentum.We also set the force in the X, Y, and Z direction to be 0: 

Let's go to the next problem on antennas. There's a very tight antenna with some little things that are tied up together. It's not uncommon for these towers to actually have it like a ball joint on the bottom. 

There are wires to hold it, and say that the antenna is on the y axis. The first wire out to c is at a point on the -x axis 50 meters, where the tower is 70 meters tall. The second wire is out in fromt with 20 meters from the z axis and 50 meters from the y axis. The third wire is at a point that's about 45 meters from the z axis and 40 meters from the x axis. Here is the following drawing: 

Figure out the reaction forces at the bottom, and as many forces as I can. Let's draw a free-body diagram. 

Normalizing the vector consists of all the components less than 1.  What if the antenna has no ball-joint and they decide to bolt it down?