Vector Products (Cross Product). Torque F r T.

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Transcript of Vector Products (Cross Product). Torque F r T.

Vector Products (Cross Product)

Torque

F

rT

Vector Products

Definition of Cross Product

Interpretation of the Cross Product (from autograph)

a

ba x b

A small proof…

Small proof continued..

The vector CROSS product

• Results in a NEW vector!

As seen on the formula booklet

Some examples

• .

But…..you do not NEED to know the matrix algebra, you just need to know how to use the IB formula.

You try!

• Use the IB formula this time:

• .

Applications of the Cross Product

• Constructing Orthogonal Vectors

• Area of a Triangle or a Parallelogram

• Volume of a Parallelepiped

• Moment of Force

• Angular Velocity

• Magnetic and Electric Fields

Cross Product of Unit Vectors

x

y

z

i

jk

Properties of the Cross Product

Cautions

Coordinate Formula

Application

Scalar Triple Product

Application