Explanation
The directories on a 64 bit Linux system that typically contain shared libraries are /usr/lib64/ and /lib64/.
Shared libraries are binary files that provide reusable functions, routines, classes, data structures, and so on for programs and applications. They are loaded into memory before the program starts and shared by multiple processes that use the same library. Shared libraries are usually stored in standard locations in the file system, such as /usr/lib, /usr/local/lib, /lib, and /lib64 for 32 bit systems, and /usr/lib64, /usr/local/lib64, /lib64, and /lib for 64 bit systems12. The /usr/lib64 and /lib64 directories contain the shared libraries for the system and user applications, respectively. The other directories are either non-existent or do not contain shared libraries. The
~/.lib64/ directory is not a standard location for shared libraries, and it is unlikely that a user would have such a directory in their home directory. The /var/lib64/ directory is also not a standard location for shared libraries, and it is usually used for variable data files that are specific to a package or application. The /opt/lib64/ directory is not a standard location for shared libraries, and it is usually used for optional software packages that are installed in the /opt directory3. References:
* Linux Essentials - Linux Professional Institute Certification Programs1
* Exam 101 Objectives - Linux Professional Institute2
* Understanding Shared Libraries in Linux - Tecmint3