We are very familiar with real valued functions, that is, functions whose output is a real number. This section introduces vector–valued functions – functions whose output is a vector.
We have already seen that a convenient way to describe a line in three dimensions is to provide a vector that "points to'' every point on the line as a parameter t varies. Except that this gives a pa...We have already seen that a convenient way to describe a line in three dimensions is to provide a vector that "points to'' every point on the line as a parameter t varies. Except that this gives a particularly simple geometric object, there is nothing special about the individual functions of t that make up the coordinates of this vector---any vector with a parameter will describe some curve in three dimensions as t varies through all possible values.
A vector-valued function of a real variable is a rule that associates a vector f(t) with a real number t, where t is in some subset D of R1 (called the domain of...A vector-valued function of a real variable is a rule that associates a vector f(t) with a real number t, where t is in some subset D of R1 (called the domain of f). We write f: D→R3 to denote that f is a mapping of D into R3 .
