Vector Products (Cross Product)

Torque

F

rT

Torque

F

rT

F1

F2

Torque

F

rT

F1

F2

||T|| = ||F1||x ||r||

Torque

F

rT

F1

F2

||T|| = ||F1||x ||r||

= ||F|| x ||r|| sin

Vector Products

Definition of Cross Product

Interpretation of the Cross Product

a

ba x b

Applications of the Cross Product

• Constructing Orthogonal Vectors

• Area of a Triangle or a Parallelogram

• Volume of a Parallelepiped

• Moment of Force

• Angular Velocity

Cross Product of Unit Vectors

x

y

z

i

jk

Properties of the Cross Product

Cautions

Coordinate Formula

Application

Scalar Triple Product

Application