Applications of the Dot Product (Projections)

Applications of the dot product is part of the Vectors topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-02). Building on the projections met in Extension 1, this subtopic uses the scalar (dot) product to split a vector into its projection along another vector plus a part perpendicular to it, in two and three dimensions.

Students and teachers will cover using projections to find the perpendicular distance from a point to a line, the foot of a perpendicular, areas of triangles and parallelograms, and the part of a force acting along a chosen direction — tools reused for resolving forces in the HSC Extension 2 mechanics topic.