9.1 Vector Functions
INTRODUCTION
Recall that a curve C in the xy-plane is simply a set of ordered pairs (x, y). We say that C is a parametric curve if the x- and y-coordinates of a point on the curve are defined by a pair of functions x = f(t), y = g(t) that are continuous on some interval a ≤ t ≤ b. The notion of a parametric curve extends to 3-space as well. A parametric curve in space, or space curve, is a set of ordered triples (x, y, z) where
x = f(t), y = g(t), z = h(t), (1)
are continuous on an interval defined by a ≤ t ≤ b. In this section we combine the concepts of parametric curves with vectors.
Vector-Valued Functions
It is often ...
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