Algebra - Geometry and measurement in two and three dimensions — Vectors in space

About this lesson

This unit introduces vectors in three-dimensional space (R3). It begins by defining the position vector of a point with respect to the origin, its components along the x, y, and z axes, and the norm (length) of a vector. It then covers vector operations: addition, scalar multiplication, and equality of vectors, along with their algebraic properties. The unit also explains the fundamental unit vectors i, j, k, how to express any vector in terms of these unit vectors, and how to express a directed line segment between two points using their coordinates. Finally, it defines the unit vector in the direction of a given vector, and introduces direction angles and direction cosines, showing how to find them and how to express a vector given its norm and direction angles. The text includes worked examples, 'try to solve' exercises, and a set of mixed exercises at the end.