              home  physics online guide physics help my info terms of use contacts    What is Physics? Mechanics Electricity and Magnetism Electric Field Gauss' Law about below subjects Electric Potential Capacity Direct Current Magnetic Field Magnetic Field Laws Magnetic Interactions Electromagnetic Induction Maxwell's Equations Oscillations and Waves Simple Harmonic Motion Damped Harmonic Motion Driven Harmonic Motion Electric Oscillation Alternating Current Wave Motion Elastic Waves Electromagnetic Waves Optics Light Waves Geometrical Optics Interference Polarization Diffraction Fraunhofer Diffraction Dispersion, Absorption, Diffusion Doppler Effect Thermodynamics Ideal Gas Molecular Statistics Transport Phenomena First Law of Thermodynamics Second and Third Laws of Thermodynamics Imperfect Gas Liquids Solids Quantum Physics Thermal Radiation Quantum Properties of Light Wave Properties of Particles Planetary Model of Atom X-Rays Particle in Potential Well Pauli Exclusion Principle Nuclear Physics Solid State Physics Appendices  # Vectors

Vector is a quantity specified by magnitude plus direction in space

## Properties of vectors

Any vector is uniquely specified by its three components x, y, z which are projections of the vector on coordinate axes with unit vectors (such that ) The notation of vector with coordinates has the form

is Magnitude of vector (or its length) is defined by Pythagorean Theorem

| | = Adding of vectors and is sum vector The sum vector is determined by Parallelogram Rule of addition Magnitude of sum vector is defined by Law of Cosines where: and are magnitudes of the vectors and  is angle between them

Components of sum vector:

x = x1+ x2

y = y1+ y2

z = z1+ z2

The parallelogram rule of addition is partial case of general Polygon Rule used for adding several vectors  ## Subtracting vectors

Subtracting of vectors and is vector difference The vector difference is determined by Triangle Method of subtraction Magnitude of vector difference Components of vector difference:

x = x1 - x2

y = y1 - y2

z = z1 - z2

## Scalar Product

Scalar (or dot) product of vectors and is scalar quantity defined by where is angle between vectors and Properties of scalar product:

1) 2) If then 3) If then 4) ## Vector product

Vector (or cross) product of vectors and is vector  The vector is normal to plane in which the vectors and lie (plane x-y) directed in accordance with Right-Hand Rule: when right palm is half-bent from to its thumb shows the direction of vector Magnitude of vector  where is angle between vectors and Components of vector product:   Properties of vector product:

1) 2) If then 3) If then magnitude of vector product is  home  |  physics online guide  |  physics help  |  my info  |  terms of use  |  contacts Dr. Nikitin © 2010       