Meeting 23Vectors

Vectors in 2-Space, 3-Space, and n-Space

We will denote vectors in boldface type such as a, b, v, w, and x, and we will denote scalars in lowercase italic type such as a, k, v, w, and x. When we want to indicate that a vector v has initial point A and terminal point B.

Vector addition as a process of translating points

Vector Subtraction

Scalar Multiplication

Vectors in CoordinateSystems

We will write v = (v1, v2) to denote a vector v in2-space with components (v1, v2), and v = (v1, v2, v3) to denote a vector v in 3-spacewith components (v1, v2, v3).

Vectors Whose Initial PointIs Not at the Origin

n-Space

Operations on Vectors in

Example

The Properties of Vector Operations

Norm of a Vector

The Properties of a Norm

Unit Vectors

Example

Dot Product

Angle between two vectors

Component Form of theDot Product

Algebraic Properties of theDot Product

Cauchy–Schwarz Inequalityand Angles in

Exercises