NSW Syllabus Reference: MEX-V1.3: Vectors and vector equations of lines. This will require student to
- use Cartesian coordinates in two and three-dimensional space
- recognise and find the equations of spheres
- use vector equations of curves in two or three dimensions involving a parameter, and determine a corresponding Cartesian equation in the two-dimensional case, where possible (ACMSM104)
- understand and use the vector equation \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{r} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{a} + \lambda \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{b} \) of a straight line through points \(A\) and \(B\) where \(R\) is a point on \(AB\), \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{a} = \overrightarrow {OA} ,\,\,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{b} = \overrightarrow {AB} ,\,\,\lambda \) is a parameter and \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{r} = \overrightarrow {OR} \)
- make connections in two dimensions between the equation \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{r} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{a} + \lambda \,\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{b} \) and \(y=mx+c\)
- determine a vector equation of a straight line or straight-line segment, given the position of two points or equivalent information, in two and three dimensions (ACMSM105)
- determine when two lines in vector form are parallel
- determine when intersecting lines are perpendicular in a plane or three dimensions
- determine when a given point lies on a given line in vector form
Ref: https://educationstandards.nsw.edu.au/
