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RE: LeoThread 2025-05-21 06:49

in LeoFinance5 months ago

Part 2/7:

Vector functions can be defined as functions that take real numbers as input and produce vectors as outputs. They extend our understanding of functions beyond the real-valued functions we are familiar with, enabling us to describe curves and surfaces in space.

The fundamental form of a vector function ( \mathbf{R}(t) ) in three-dimensional space can be expressed as:

[

\mathbf{R}(t) = \langle f(t), g(t), h(t) \rangle

]

where ( f(t), g(t), ) and ( h(t) ) are real-valued functions that correspond to the x, y, and z coordinates respectively. This definition allows us to visualize complex curves, such as in orbital mechanics or computer graphics, where objects travel along paths defined by vector functions.


Limits of Vector Functions