A100-lb load hangs from three cables of equal length that are anchored at the points (minus4,0,0), (2,2 startroot 3 endroot,0), and (2,minus2 startroot 3 endroot,0). the load is located at (0,0,minus4 startroot 3 endroot). find the vectors describing the forces on the cables due to the load.

Explanation:

The mass of the load is

As the mass hangs, the cables must be tight, so, we can obtain the vector parallel to the cable as:

where is the position of the load and  is the point where the cable is anchored.

So, for our cables

We know that the forces must be in this directions, so we can write

We also know, as the system is in equilibrium, the sum of the forces must be zero:

where is the weight,

So, we get:

This gives us the following equations:

From equation [2] is clear that , we can see that

Now, putting this in equation [1]

Taking this result to the equation [3]

So, the forces are:

a and b sometimes have a positive value