The proper way to do this is like this:
LIBS += -L/path/to -lpsapi
This way it will work on all platforms supported by Qt. The idea is that you have to separate the directory from the library name (without the extension and without any 'lib' prefix). Of course, if you are including a Windows specific lib, this really doesn't matter.
In case you want to store your lib files in the project directory, you can reference them with the $$_PRO_FILE_PWD_
variable, e.g.:
LIBS += -L"$$_PRO_FILE_PWD_/3rdparty/libs/" -lpsapi
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