A vector in two-dimensional space is a pair \(\langle x,y \rangle\) that, without any other context, denotes movement from the origin to the point \((x,y).\) \(x\) and \(y\) are called the horizontal and vertical components of the vector. Sometimes we talk about the vector from a point \(A\) to a point \(B,\) which we’ll denote \(\overrightarrow{AB}.\) The points \(A\) and \(B\) are referred to as the initial and terminal points respectively. The length of a vector \(\bm{v}\) is referred to as its magnitude, and is denoted \(|\bm{v}|.\) (the txt uses u and v as generic vectors) Vectors have direction and magnitude. Think of a vector as a displacement. Define unit vector. Define the unit coordinate vectors \(\mathbf{i}\) and \(\mathbf{j},\) and note that \(\langle x,y \rangle = x\mathbf{i} + y\mathbf{j}.\)
The zero vector \(\bm{0}.\)
addition of vectors (sum of displacements). scalar multiplication of a vector (scaling).
We now refer to numbers as scalars to differentiation them from vectors.
Vectors model velocities or forces. The resultant force is the sum of multiple forces acting on an object.