Troubleshooting Vector Angles in Three Dimensions

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The discussion revolves around troubleshooting vector angles in three dimensions, specifically questioning the accuracy of provided answers in a textbook. The user believes their calculated angles, β=52.5, α=121, and γ=53.1, are correct but suspects the textbook may be wrong. They express confusion over the similarity of their results to the book's answers while noting that the gamma angles match. The user seeks clarity on potential errors in their approach to solving the problem. Overall, the thread highlights a common challenge in verifying solutions to complex vector angle problems.
whynot314
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ok so I am not sure how else to do this problem, my answers look similar to those in the book. where they have β=52.5 \alpha=121 \gamma=53.1, I feel like the book is wrong because i don't see any other way to solve this problem.

[URL=http://s1341.photobucket.com/user/nebula-314/media/20130523_174427_zpsda388c38.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130523_174427_zpsda388c38.jpg[/URL][/PLAIN]

Heres how I solved for the angles
[URL=http://s1341.photobucket.com/user/nebula-314/media/20130523_174442_zps9be6b8d1.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130523_174442_zps9be6b8d1.jpg[/URL][/PLAIN]
 
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The gammas are the same so I am unsure where I went wrong.
 

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