After 2 semesters of calculus concentrating on curves of the form *y* = *f*(*x*) , our next task is to extend what we have learned to the curves
and surfaces which reside in 3 dimensional space. However, moving from one
point on a line to another in 3 dimensions involves a rise up or down, a run
forward or back, and a slide left or right. Slope only involves a rise and a
run, thus making it strictly a 2 dimensional concept.

Thus, we begin this chapter by replacing the concept of slope with the
concept of a *vector. *We then see that the study of curves in space is
mathematically equivalent to the study of vectors and functions involving
vectors. Indeed, the use of vectors allows us to introduce the fundamental
concepts of velocity and acceleration in their true form, thus allowing us
to study velocity and acceleration in their native form.

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