Cambridge O Level Mathematics (Syllabus D) · Syllabus 4024 · Transformations and Vectors
Vectors in Two Dimensions
What is Vectors in Two Dimensions?
A vector in two dimensions is a quantity with both magnitude and direction, recorded as a column vector whose top entry is the horizontal displacement and whose bottom entry is the vertical displacement. Cambridge prints vectors either as a directed line segment such as AB with an arrow above it, or as a lower case bold letter such as a. A vector fixes a movement but not a starting point, so two arrows of the same length and direction anywhere in the plane represent the same vector. Vectors are added and subtracted entry by entry and multiplied by a scalar entry by entry, so k times the column x, y is the column kx, ky. Reversing a directed segment reverses its vector, giving BA equal to minus AB, and following one directed segment by another gives the route rule AB plus BC equals AC. When the position vectors of A and B from an origin O are a and b, the route from A through O to B gives AB equal to b minus a, with the subtraction always in that order. A column vector is also exactly what describes a translation, which is why the same notation serves both halves of this topic.
This definition is part of the Transformations and Vectors chapter in Cambridge O Level Mathematics (Syllabus D).