Often when working with moving objects it is helpful to be able to find out if they will collide, this can be done by using space curves and multivariable calculus.
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The tangent vector to a space curve that represents an objects position in space yields the object's velocity at that time and position.
Given two space curve vectors that represent the paths of two different objects one can find out if/when/where they intersect by setting each of their components equal to each other.
See Multivariable Calculus Notes - Chapter 13 - Sections 1-2 for examples and more information.