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    • What is the velocity vector in polar coord...   Acceleration in polar coordinates    • What is the acceleration vector in polar c...   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