Further work with Vectors

This topic develops students’ ability to use vectors as a powerful tool for modelling and solving geometric problems in both two and three dimensions. Students learn how to represent straight lines and curves using vector equations, understand direction vectors and parameters, and determine properties such as parallel lines, intersections, collinearity, and skew lines in three-dimensional space. They also explore parametric vector equations for curves, including circles and spheres, and convert between vector and Cartesian forms. In addition, students apply vector techniques to geometry by using the scalar (dot) product, vector properties, and inequalities such as the Cauchy–Schwarz inequality to solve problems and prove geometric results involving triangles, distances, angles, and other spatial relationships.