what is the meaning of coriolis force

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  The observed effect of the Coriolis force, especially the deflection of objects or substances (such as air) moving along the surface of the Earth, rightward in the Northern Hemisphere and leftward in the Southern Hemisphere. The Coriolis effect is named after the French engineer Gustave Gaspard Coriolis (1792-1843).

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I was going through the concepts of Coriolis force but got stuck at the point that the Coriolis force is zero at the equator. Consider a person moving along the equator with a velocity v. Mathematically,Coriolis force= -2m(w x v)In this case though the latitude is zero, the angular velocity vector and the tangential velocity vector are perpendicular. This gives a non zero Coriolis force! I know something is wrong with my reasoning but can't figure it out. The only way out seems that that the 2 vectors are not perpendicular. Something to do with angle between 2 lines in 3-D space?

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