Mechanics Statics: Vector Manipulations Problem

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ur5pointos2sl
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This is just an entry level problem from the second day of class. It isn't really dealing with statics but with just vector manipulations. I have included a copy of the problem and a partial attempt. Any help would be appreciated.
 
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  • Handwritten statics solution on graph paper: a 3D coordinate sketch with forces F1 = 12 kN and F2 = 10 kN, a 30-degree angle, and vector sums for F3 with resultant magnitude 13.568 kN.
    work3.jpg
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  • Textbook diagram of a pipe fixed at a flange on the x-z plane, with three forces: F1 = 12 kN and F2 = 10 kN acting in the x-y plane, and an unknown force F3 with angles alpha3, beta3 and gamma3 marked to the axes.
    7.21y.jpg
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3d vectors can drive you insane! I think you did a real good job, except that F1z should be a minus 6, not +6. I might have missed something else, but your approach is excellent.
 
PhanthomJay said:
3d vectors can drive you insane! I think you did a real good job, except that F1z should be a minus 6, not +6. I might have missed something else, but your approach is excellent.

Thank you for your reply. While waiting on my attachments to get approved I actually have solved the problem. I did notice that +6 should've been -6 and also when summing the forces for F3 I needed -cos alpha and -cos gamma. Thanks again.