Vector Equations of Curves

Vector equations of curves is part of the Vectors topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-02). This subtopic recognises that a parametrically defined curve can be written as a vector equation \(\mathbf{r} = \begin{pmatrix} x(t) \\ y(t) \end{pmatrix}\), where \(t\) is a parameter, in two and three dimensions.

Students and teachers will cover how to identify a curve from its vector equation, write the vector equation of a curve from its graph, and determine the Cartesian equation of a curve from its vector form — connecting parametric and Cartesian descriptions in the HSC Extension 2 course.