(a) Starting with the vector form, write out each component of the momentum equation in terms
of the zonal (ˆi), meridional (ˆj), and vertical (ˆk) directions. Include the appropriate acceleration
term on the left-hand side of each equation. Use the Coriolis parameter (f) to account for latitudinal
variations in rotation rate Ω about the local vertical. (b) Explain why the zonal and meridional
components of Coriolis force have different signs (you can use the right-hand rule or evaluate the
3x3 determinant for the cross product).