which unit vector points in the positive direction of the z axis
Unit vector The unit vectors appropriate to spherical symmetry are:    r ^   {\displaystyle \mathbf {\hat {r}} } , the direction in which the radial distance from the origin increases;    φ ^   {\displaystyle {\boldsymbol {\hat {\varphi }}}} , the direction in which the angle in the x-y plane counterclockwise from the positive x-axis is increasing; and    θ ^   {\displaystyle {\boldsymbol {\hat {\theta }}}} , the direction in which the angle from the positive z axis is increasing. To minimize redundancy of representations, the polar angle   θ  {\displaystyle \theta }  is usually taken to lie between zero and 180 degrees. It is especially important to note the context of any ordered triplet written in spherical coordinates, as the roles of    φ ^   {\displaystyle {\boldsymbol {\hat {\varphi }}}}  and    θ ^   {\displaystyle {\boldsymbol {\hat {\theta }}}}  are often reversed. Here, the American "physics" convention[1] is used. This leaves the azimuthal angle   φ  {\displaystyle \varphi }  defined the same as in cylindrical coordinates. The Cartesian relations are:
North Pole The North Pole is the northernmost point on the Earth, lying diametrically opposite the South Pole. It defines geodetic latitude 90Â° North, as well as the direction of true north. At the North Pole all directions point south; all lines of longitude converge there, so its longitude can be defined as any degree value. Along tight latitude circles, counterclockwise is east and clockwise is west. The North Pole is at the center of the Northern Hemisphere.