Vector-valued function

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A graph of the vector-valued function <2Cos(t),4Sin(t),t>
A graph of the vector-valued function <2Cos(t),4Sin(t),t>

A vector-valued function is a mathematical function that maps real numbers onto vectors. Vector-valued functions can be defined as:

  • \mathbf{r}(t)=f(t)\mathbf{{\hat{i}}}+g(t)\mathbf{{\hat{j}}} or
  • \mathbf{r}(t)=f(t)\mathbf{{\hat{i}}}+g(t)\mathbf{{\hat{j}}}+h(t)\mathbf{{\hat{k}}}

where f(t), g(t) and h(t) are functions of the parameter t and i, j and k are unit vectors. Vector functions can also be referred to in a different notation:

  • \mathbf{r}(t)=\langle f(t), g(t)\rangle or
  • \mathbf{r}(t)=\langle f(t), g(t), h(t)\rangle

[edit] Properties

The domain of a vector-valued function is the intersection of the domain of the functions f, g and h.

[edit] See also

[edit] External links

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