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    • 1 Foundations >
      • 1.1 Dimensions and units
      • 1.2 Mathematic skills
      • 1.3 Graphing
      • 1.4 Vectors
      • 1.5 Vectors in 3D
    • 2 Mechanics >
      • 2.1 Kinematics 1D >
        • 2.1.1 Kinematics Intro
        • 2.1.2 Acceleration
        • 2.1.3 Graphing Motion
        • 2.1.4 Equations of Motion
      • 2.2 Kinematics 2D >
        • 2.2.1 Relative Motion
        • 2.2.2 Projectile Motion
      • 2.3 Forces >
        • 2.3.1 Newton's Laws
        • 2.3.2 forces in equilibrium
        • 2.3.3 Normal
        • 2.3.4 Friction
        • 2.3.5 Forces and Pulleys
      • 2.4 Momentum and Energy >
        • 2.4.1 Momentum
        • 2.4.2 Energy
      • 2.5 Rotational Mechanics >
        • 2.5.1 Circular Motion
        • 2.5.2 Angular Velocity
        • 2.5.3 Circular applications
        • 2.5.4 Moment of Inertia
        • 2.5.5 Torque
      • 2.6 Gravity >
        • 2.6.1 Gravitation
        • 2.6.2 Orbital Motion
        • 2.6.3 Kepler's Laws
        • 2.6.4 Gravitation and Energy
    • 3 Waves and Optics >
      • 3.1 Wave Phenomena >
        • 3.1.1 Wave Types
        • 3.1.2 Superposition
        • 3.1.3 Interference
        • 3.1.4 Inverse Square Law
        • 3.1.5 Modulation
      • 3.2 Sound >
        • 3.2.1 Beats
        • 3.2.2 Doppler
        • 3.2.3 Resonance
        • 3.2.4 Standing Waves
      • 3.3 Physical Optics >
        • 3.3.1 Light - a history
        • 3.3.2 Double Slit Diffraction
        • 3.3.3 Light - its speed
        • 3.3.4 Light as EMR
        • 3.3.5 Polarisation
        • 3.3.6 Spectroscopy
        • 3.3.7 Scattering
      • 3.4 Geometric Optics >
        • 3.4.1 Reflection
        • 3.4.2 Refraction
        • 3.4.3 Lenses and Images
        • 3.4.4 Dispersion
    • 4 Thermodynamics >
      • 4.1 Heat and Temperature
      • 4.2 Specific Heat Capacity
      • 4.3 Latent Heat
      • 4.4 Blackbody Radiation
    • 5 Electricity and Magnetism >
      • 5.1 Electrostatics >
        • 5.1.1 Charge
        • 5.1.2 Coulomb's Law
        • 5.1.3 Electric Field
        • 5.1.4 Voltage
      • 5.2 Circuits >
        • 5.2.1 Ohm's Law
        • 5.2.2 Series and Parallel Circuits
        • 5.2.3 Electrical Power
      • 5.3 Electromagnetism >
        • 5.3.1 Moving Charges in Electric Fields
        • 5.3.2 Ampere's Law
        • 5.3.3 Charge in Magnetic Fields
        • 5.3.4 Motor Effect
        • 5.3.5 DC Motor
      • 5.4 Electromagnetic Induction >
        • 5.4.1 Magnetic Flux
        • 5.4.2 Faraday's Law
        • 5.4.3 Lenz' Law
        • 5.4.4 Back EMF
        • 5.4.5 Generators
        • 5.4.6 Transformers
        • 5.4.7 Induction Motors
    • 6 Modern Physics >
      • 6.1 Relativity >
        • 6.1.1 Michelson Morley Experiment
        • 6.1.2 Special Relativity
        • 6.1.3 Special Relativity Evidence
      • 6.2 Atomic Physics >
        • 6.2.1 JJ Thomson and the electron
        • 6.2.2 Millikan
        • 6.2.3 Rutherford
        • 6.2.4 Chadwick
      • 6.3 Radioactivity >
        • 6.3.1 What is Radioactivity
        • 6.3.2 Half Life
        • 6.3.3 Binding Energy
        • 6.3.4 Strong Nuclear Force
        • 6.3.5 Fission
        • 6.3.6 Fusion
      • 6.4 Quantum Physics >
        • 6.4.1 Planck and the Blackbody
        • 6.4.2 Photoelectric Effect
        • 6.4.3 Bohr Model
        • 6.4.4 de Broglie and Matter Waves
        • 6.4.5 Compton Effect
        • 6.4.6 Schrödinger Equation
        • 6.4.7 Heisenberg
        • 6.4.8 Lasers
      • 6.4 Particle Physics
      • 6.5 Solid State Physics
    • 7 Astrophysics >
      • 7.1 Olber's Paradox
      • 7.2 Stellar Spectroscopy
      • 7.3 Determining Stellar Distances
      • 7.4 Star Magnitude
      • 7.5 Star Temperature
      • 7..6 HR Diagram
    • 8 Medical Physics >
      • 8.1 Ultrasound
      • 8.2 X-ray
      • 8.3 PET scans
      • 8.4 MRI
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Vectors advanced

PREVIOUS LESSON                                                                                                                                        NEXT LESSON
 
The previous lesson examines vectors in two dimension only and we only examine the addition (and subtraction) of vectors 
However, vectors can be represented in three dimensions. They can also be multiplied.

In these of lesson, we will examine how to manipulate vectors with these considerations.


To start off, we ned to learn a new way of representing vectors. This allows for a simpler way to do various operations.
This video examines to concept of unit vectors 



Now that we covered unit vectors we can introduce multiplication of vectors 
However, there are two ways that vectors can be multiplied - the dot product and cross product

These two videos examines the two processes and provides examples of where they are used

 
PREVIOUS LESSON                                                                                                                                        NEXT LESSON

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  • Home
  • Lessons
    • 1 Foundations >
      • 1.1 Dimensions and units
      • 1.2 Mathematic skills
      • 1.3 Graphing
      • 1.4 Vectors
      • 1.5 Vectors in 3D
    • 2 Mechanics >
      • 2.1 Kinematics 1D >
        • 2.1.1 Kinematics Intro
        • 2.1.2 Acceleration
        • 2.1.3 Graphing Motion
        • 2.1.4 Equations of Motion
      • 2.2 Kinematics 2D >
        • 2.2.1 Relative Motion
        • 2.2.2 Projectile Motion
      • 2.3 Forces >
        • 2.3.1 Newton's Laws
        • 2.3.2 forces in equilibrium
        • 2.3.3 Normal
        • 2.3.4 Friction
        • 2.3.5 Forces and Pulleys
      • 2.4 Momentum and Energy >
        • 2.4.1 Momentum
        • 2.4.2 Energy
      • 2.5 Rotational Mechanics >
        • 2.5.1 Circular Motion
        • 2.5.2 Angular Velocity
        • 2.5.3 Circular applications
        • 2.5.4 Moment of Inertia
        • 2.5.5 Torque
      • 2.6 Gravity >
        • 2.6.1 Gravitation
        • 2.6.2 Orbital Motion
        • 2.6.3 Kepler's Laws
        • 2.6.4 Gravitation and Energy
    • 3 Waves and Optics >
      • 3.1 Wave Phenomena >
        • 3.1.1 Wave Types
        • 3.1.2 Superposition
        • 3.1.3 Interference
        • 3.1.4 Inverse Square Law
        • 3.1.5 Modulation
      • 3.2 Sound >
        • 3.2.1 Beats
        • 3.2.2 Doppler
        • 3.2.3 Resonance
        • 3.2.4 Standing Waves
      • 3.3 Physical Optics >
        • 3.3.1 Light - a history
        • 3.3.2 Double Slit Diffraction
        • 3.3.3 Light - its speed
        • 3.3.4 Light as EMR
        • 3.3.5 Polarisation
        • 3.3.6 Spectroscopy
        • 3.3.7 Scattering
      • 3.4 Geometric Optics >
        • 3.4.1 Reflection
        • 3.4.2 Refraction
        • 3.4.3 Lenses and Images
        • 3.4.4 Dispersion
    • 4 Thermodynamics >
      • 4.1 Heat and Temperature
      • 4.2 Specific Heat Capacity
      • 4.3 Latent Heat
      • 4.4 Blackbody Radiation
    • 5 Electricity and Magnetism >
      • 5.1 Electrostatics >
        • 5.1.1 Charge
        • 5.1.2 Coulomb's Law
        • 5.1.3 Electric Field
        • 5.1.4 Voltage
      • 5.2 Circuits >
        • 5.2.1 Ohm's Law
        • 5.2.2 Series and Parallel Circuits
        • 5.2.3 Electrical Power
      • 5.3 Electromagnetism >
        • 5.3.1 Moving Charges in Electric Fields
        • 5.3.2 Ampere's Law
        • 5.3.3 Charge in Magnetic Fields
        • 5.3.4 Motor Effect
        • 5.3.5 DC Motor
      • 5.4 Electromagnetic Induction >
        • 5.4.1 Magnetic Flux
        • 5.4.2 Faraday's Law
        • 5.4.3 Lenz' Law
        • 5.4.4 Back EMF
        • 5.4.5 Generators
        • 5.4.6 Transformers
        • 5.4.7 Induction Motors
    • 6 Modern Physics >
      • 6.1 Relativity >
        • 6.1.1 Michelson Morley Experiment
        • 6.1.2 Special Relativity
        • 6.1.3 Special Relativity Evidence
      • 6.2 Atomic Physics >
        • 6.2.1 JJ Thomson and the electron
        • 6.2.2 Millikan
        • 6.2.3 Rutherford
        • 6.2.4 Chadwick
      • 6.3 Radioactivity >
        • 6.3.1 What is Radioactivity
        • 6.3.2 Half Life
        • 6.3.3 Binding Energy
        • 6.3.4 Strong Nuclear Force
        • 6.3.5 Fission
        • 6.3.6 Fusion
      • 6.4 Quantum Physics >
        • 6.4.1 Planck and the Blackbody
        • 6.4.2 Photoelectric Effect
        • 6.4.3 Bohr Model
        • 6.4.4 de Broglie and Matter Waves
        • 6.4.5 Compton Effect
        • 6.4.6 Schrödinger Equation
        • 6.4.7 Heisenberg
        • 6.4.8 Lasers
      • 6.4 Particle Physics
      • 6.5 Solid State Physics
    • 7 Astrophysics >
      • 7.1 Olber's Paradox
      • 7.2 Stellar Spectroscopy
      • 7.3 Determining Stellar Distances
      • 7.4 Star Magnitude
      • 7.5 Star Temperature
      • 7..6 HR Diagram
    • 8 Medical Physics >
      • 8.1 Ultrasound
      • 8.2 X-ray
      • 8.3 PET scans
      • 8.4 MRI
  • curriculum specific
    • NSW >
      • NSW curriculum >
        • Year 11
        • Year 12
      • HSC question per Module
      • HSC Exam review >
        • Downloads/notes
    • QLD curriculum
    • IB curriculum
    • SAT curriculum
    • AP Physics 1&2 curriculum
  • Resources
    • Review videos
    • Shorts
    • Formula Sheet
    • tools >
      • Calculator
      • Oscilloscope
    • data sheet
    • for students >
      • recommended physics sites
      • Review and Tips
    • for teachers
    • Blogs >
      • Podcasts
      • PhysicsHigh blog
    • About >
      • Who am I
      • FAQ
      • Fun
      • Contact