Meeting 23 Vectors

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 Coordinate Systems We will write v = (v 1, v 2 ) to denote a vector v in 2-space with components (v 1, v 2 ), and v = (v 1, v 2, v 3 ) to denote a vector v in 3-space with components (v 1, v 2, v 3 ).

Vectors Whose Initial Point Is Not at the Origin

n-Space

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 the Dot Product

Algebraic Properties of the Dot Product

Exercises