Calculus 3: Vector Functions

Find the derivative of the vector-valued function $\mathbf{R}(t) = (f(t), g(t), h(t))$ where $f$, $g$, and $h$ are scalar functions.

Describe a curve using a position vector-valued function.

Using vector valued functions, describe the path of a particle or object, taking into account time as a variable.

Parametrize the same curve using different rates and understand the derivative of a position vector valued function.

Describe the path of a particle in three-dimensional space using vector valued functions.

Give an example of a vector-valued function r(t) and determine its domain and range in $R^3$.