Vector Products (Dot Product)

Vector Algebra

The Three Products

Work

F

d

Work

F

Fh Fv d

Work

F

Fh Fv d

Work = ||Fh||x ||d||

Work

F

Fh Fv d

Work = ||Fh||x ||d||

= ||F|| x ||d|| cos

Dot Product

Work

F

Fh d

Application

Theorem

Alternate Definition

Properties of the Dot Product

Length or Magnitude

Application

Angle Between Vectors

Application

Component of Projection

v

u

Projection of a Vector

v

u

Pproj

Application

Direction Cosines

Application