Resolve each force acting on the gusset plate into its x and y components, and express each force as a Cartesian vector.

#### Solution:

### To do this question, it’s best to draw each vector component separately and to also break apart the force into it’s x and y components.

### This is the force F_3. Remember that we can translate the force along it’s path, hence we drew the downwards force originating from the center of our coordinate system so that it’s easier to visualize.

### This is force F_2.

### And finally, this is force F_1 which is simply a force that is only along the positive x-axis.

### In each diagram, we also broke the force into it’s x and y vector components. For force F_1 the y component is simply 0 because the force lies along the positive x-axis.

### After breaking apart the vectors, we can write them using the i,j,k Cartesian vector coordinate system.

### Looking at force F_1, we can see that it only lies along the i plane. Thus, we have:

### \vec{F_1} = \left\{{900i}\right\}N

### For force F_2, there are two components, i and j. We can write the following for force F_2:

### \vec{F_2} = \left\{750\cos 45^0(i) + 750\sin 45^0(j)\right\}N

### \vec{F_2} =\left\{530i + 530j\right\}N