This IB Maths AA AHL Topic 3.12 – Introduction to Vectors resource introduces students to the key properties, notation, and applications of vectors in two and three dimensions. It begins by defining a vector in terms of magnitude and direction and showing how vectors can be represented geometrically, using components, or as linear combinations of base vectors. Students learn how to calculate vector magnitudes and directions, work with position vectors, and interpret vectors as movements between points.

The lesson then develops fluency in adding and subtracting vectors using both component methods and geometric approaches such as the tip-to-tail and parallelogram methods. Students explore zero vectors, negative vectors, scalar multiples, parallel vectors, and unit vectors, including how to normalize a vector by dividing it by its magnitude. The resource also introduces displacement vectors and shows how vector algebra can be used to prove geometric properties such as collinearity, equal and parallel sides, midpoints, and parallelograms. With clear diagrams, formula summaries, worked examples, geometric interpretations, proof-style questions, and fully worked solutions, this resource helps AHL students build a strong foundation in vectors in line with IB Mathematics AA expectations.