Cylindrical unit vectors are defined in a cylindrical coordinate system, consisting of the radial unit vector (\hat{r}), the angular unit vector (\hat{\theta}), and the vertical unit vector (\hat{z}). Graphically, (\hat{r}) points outward from the axis, (\hat{\theta}) is tangent to the circular path in the plane, and (\hat{z}) is aligned with the vertical axis. In contrast, spherical unit vectors represent a spherical coordinate system, comprising the radial unit vector (\hat{r}), the polar angle unit vector (\hat{\theta}), and the azimuthal angle unit vector (\hat{\phi}). Here, (\hat{r}) points radially outward, (\hat{\theta}) is tangent to the surface of the sphere in the direction of increasing polar angle, and (\hat{\phi}) is tangent in the direction of increasing azimuthal angle, enveloping the radial direction.
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