Unit vectors in cylindrical and spherical coordinates

How do you find the unit vectors in cylindrical and spherical coordinates in terms of the cartesian unit vectors? Lots of math. Related video velocity in polar coordinates https://youtu.be/AxlSzLPKaAU Acceleration in polar coordinates https://youtu.be/m3NUa9hhTIU 00:00 - Intro 01:07 - Position Vector 01:36 - Cylindrical coordinates 02:53 - Finding r-hat 04:25 - Finding theta-hat 06:46 - z-hat, PLEASE 07:46 - Spherical coordinates 11:47 - Finding r-hat 13:47 - Finding theta-hat 17:06 - Finding phi-hat