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- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/11%3A_Vector-Valued_Functions/11.01%3A_VectorValued_FunctionsWe 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.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_(Guichard)/13%3A_Vector_Functions/13.01%3A_Space_CurvesWe 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.
- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/01%3A_Vectors_in_Euclidean_Space/1.08%3A_Vector-Valued_FunctionsA 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 .
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_by_David_Guichard_(Improved)/13%3A_Vector_Functions/13.01%3A_Space_CurvesWe 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.