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Understanding Vector Functions and Their Applications

Vector functions are an essential aspect of calculus that extend the concept of standard real-valued functions by incorporating vectors into their framework. This article explores vector functions, their significance, and how they apply to real-world scenarios such as planetary motion governed by Kepler's laws.

What are Vector Functions?

At its core, a vector function is a rule that associates a set of real numbers (the domain) with a vector output (the range). Typically, the domain comprises real numbers represented by a parameter, often denoted as ( t ). This parameter can be thought of as time in many physical scenarios.