include path 는 어디서 정해 지는 거죠?

gcc로 가정하고 설명하면,

태영님이 말씀하신 것처럼 -I option을 써서 지정할 수 있으며 (여러 디렉토리를 지정하기 위해, 여러 번 사용 가능), C_INCLUDE_PATH 환경 변수를 써서 지정할 수도 있습니다 (포맷은 PATH와 동일).
참고로 C++ include path를 지정하기 위해서 CPLUS_INCLUDE_PATH를 쓰기도 합니다.

실제 gcc가 어떤 path에서 헤더 파일을 읽어오는지 알고 싶다면, gcc를 실행할 때 -v option을 쓰면 됩니다:

$ cat hello.c
#include <stdio.h>
 
int
main(void)
{
  printf("hello, world\n");
  return 0;
}
 
$ gcc -v hello.c
Reading specs from /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/specs
Configured with: /var/tmp/portage/gcc-3.3.5-r1/work/gcc-3.3.5/configure --enable-version-specific-runtime-libs --prefix=/usr --bindir=/usr/i686-pc-linux-gnu/gcc-bin/3.3.5 --includedir=/usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/include --datadir=/usr/share/gcc-data/i686-pc-linux-gnu/3.3.5 --mandir=/usr/share/gcc-data/i686-pc-linux-gnu/3.3.5/man --infodir=/usr/share/gcc-data/i686-pc-linux-gnu/3.3.5/info --with-gxx-include-dir=/usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/include/g++-v3 --host=i686-pc-linux-gnu --disable-altivec --enable-nls --without-included-gettext --enable-__cxa_atexit --enable-clocale=gnu --with-system-zlib --disable-checking --disable-werror --disable-libunwind-exceptions --enable-shared --enable-threads=posix --disable-multilib --disable-libgcj --enable-languages=c,c++,f77
Thread model: posix
gcc version 3.3.5  (Gentoo Linux 3.3.5-r1, ssp-3.3.2-3, pie-8.7.7.1)
 /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/cc1 -quiet -v -D__GNUC__=3 -D__GNUC_MINOR__=3 -D__GNUC_PATCHLEVEL__=5 hello.c -quiet -dumpbase hello.c -auxbase hello -version -o /tmp/ccV5z9jh.s
GNU C version 3.3.5  (Gentoo Linux 3.3.5-r1, ssp-3.3.2-3, pie-8.7.7.1) (i686-pc-linux-gnu)
        compiled by GNU C version 3.3.5  (Gentoo Linux 3.3.5-r1, ssp-3.3.2-3, pie-8.7.7.1).
GGC heuristics: --param ggc-min-expand=90 --param ggc-min-heapsize=113145
ignoring nonexistent directory "/usr/local/include"
ignoring nonexistent directory "/usr/i686-pc-linux-gnu/include"
#include "..." search starts here:
#include <...> search starts here:
 /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/include
 /usr/include
End of search list.
 /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/../../../../i686-pc-linux-gnu/bin/as -V -Qy -o /tmp/cck4wARC.o /tmp/ccV5z9jh.s
GNU assembler version 2.15.92.0.2 (i686-pc-linux-gnu) using BFD version 2.15.92.0.2 20040927
 /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/collect2 --eh-frame-hdr -m elf_i386 -dynamic-linker /lib/ld-linux.so.2 /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/../../../crt1.o /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/../../../crti.o /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/crtbegin.o -L/usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5 -L/usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/../../../../i686-pc-linux-gnu/lib -L/usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/../../.. /tmp/cck4wARC.o -lgcc -lgcc_eh -lc -lgcc -lgcc_eh /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/crtend.o /usr/lib/gcc-lib/i686-pc-linux-gnu/3.3.5/../../../crtn.o
$ _