Is it legally okay to photocopy solutions from a solutions manual when giving answers to students? I am the TA for a class and we plan on assigning problems from a book. The professor also has the solutions manual for this book. 

Would any legal problems arise if, instead of writing the solutions myself, I simply photocopied the relevant solutions from the manual and posted these on our private class webpage?
Legally?  Dunno.  I'm not a lawyer and the test for fair use is anyway not a bright line test.

Pedagogically, it will be far better to give answers that relate to how the course was taught, and it might be possible to generate those from the publisher's manual without much trouble.  Pick something discussed in class, relate it to the current problem, and explain how one gets to the solution.

Also, see both comments to the question by Nate Eldredge.