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Vector Products (Cross Product)

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Page 1: Vector Products (Cross Product). Torque F r T

Vector Products (Cross Product)

Page 2: Vector Products (Cross Product). Torque F r T

Torque

F

rT

Page 3: Vector Products (Cross Product). Torque F r T
Page 4: Vector Products (Cross Product). Torque F r T
Page 5: Vector Products (Cross Product). Torque F r T

Vector Products

Page 6: Vector Products (Cross Product). Torque F r T

Definition of Cross Product

Page 7: Vector Products (Cross Product). Torque F r T
Page 8: Vector Products (Cross Product). Torque F r T
Page 9: Vector Products (Cross Product). Torque F r T

Interpretation of the Cross Product (from autograph)

a

ba x b

Page 10: Vector Products (Cross Product). Torque F r T

A small proof…

Page 11: Vector Products (Cross Product). Torque F r T

Small proof continued..

Page 12: Vector Products (Cross Product). Torque F r T

The vector CROSS product

• Results in a NEW vector!

As seen on the formula booklet

Page 13: Vector Products (Cross Product). Torque F r T

Some examples

• .

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

Page 14: Vector Products (Cross Product). Torque F r T

You try!

• Use the IB formula this time:

Page 15: Vector Products (Cross Product). Torque F r T
Page 16: Vector Products (Cross Product). Torque F r T
Page 17: Vector Products (Cross Product). Torque F r T

• .

Page 18: Vector Products (Cross Product). Torque F r T

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

Page 19: Vector Products (Cross Product). Torque F r T

Cross Product of Unit Vectors

x

y

z

i

jk

Page 20: Vector Products (Cross Product). Torque F r T

Properties of the Cross Product

Page 21: Vector Products (Cross Product). Torque F r T

Cautions

Page 22: Vector Products (Cross Product). Torque F r T

Coordinate Formula

Page 23: Vector Products (Cross Product). Torque F r T

Application

Page 24: Vector Products (Cross Product). Torque F r T

Scalar Triple Product

Page 25: Vector Products (Cross Product). Torque F r T

Application


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