Having transitioned to OS X Mavericks and XCode 5.0.1, I can no longer gracefully link compiled C files (output from gcc) to a C++ project (output from g++).
Adding a "-x c" (without quotes) before "vec.c" should fix it.
If you compile multiple .c/.cpp files in the same line you can use "-x c" or "-x c++" before each list of C or C++ filenames to switch context appropriately. For example: