How to Find the Cross Product

As cross product or the vector product is a binary operation between two vectors in three-dimensional vector space, knowing how to find the cross product is useful. The cross product of two vector results in another vector perpendicular to the plane containing first two vectors. In general, cross product or vector product is symbolized by multiplication sign, but the mathematical operation is more advanced than simple algebraic multiplication.

The cross product of vectors and is denoted as and produces another vector , which is perpendicular to both and .

find the cross product 01

where θ is the angle measured from   to and η is the unit vector in the direction perpendicular to the plane containing both and .

Geometrically, the magnitude of the cross product of two vectors is equal to the area of a parallelogram with and as adjacent sides. Vectors , and for a right-handed system as follows:

How to find the cross product

The cross product has the following algebraic properties. 

How to Find the Cross Product_03

Following Results also hold for cross product.

How to Calculate the Cross Product

How to find the Cross Product

Vectors are often given in terms of components within a coordinate system. When given in such form, it is convenient to use determinants to calculate the cross product. 

How to Find the Cross Product_05

 Above result is for the Cartesian coordinates.

How to find the cross product – Examples 

How to find the cross product Examples

Hence, cross product is not commutative.

About the Author: admin

Leave a Comment


Related pages


difference between a cougar and a pantherbutterscotch vs carameldifference between canker sores and cold soresvalence electron definitionfriction static and kineticstatic friction and kinetic frictionthe definition of sliding frictionexample of nonpolar moleculesexamples of synesthesiamotif in literature definitioncompare a series and parallel circuitintramolecular hydrogen bondingidiom and phrasevascular and non vasculardifference between annealing and hardeningrelish vs chutneycompare prokaryotic chromosomes with eukaryotic chromosomesmarginal costing methodmitosis in plants vs animalsdefinition of centrosomespolar second moment of inertiahow to analyze poemhow does the tyndall effect workbimary fissiondifference between schizophrenia and didprecision of a vernier caliperperfume vs colognewhat is the difference between port and harbourfission buddingteeth meaning in hindidifference between lake and pondimminent eminentsimilarities between balanced and unbalanced forcesvoice pronunciation and enunciationindian smoochingmodernism versus postmodernismwhat is cytoplasms functionexamples of antithesis in literatureonomatopoeia examples sentencenatural biodegradable polymers examplesmerchant of venice monologuesspectrocolorimeter vs spectrophotometerbadger and honeyguide birdexample of assimilation in psychologydifference between a parallel circuit and a series circuit2 examples of homogeneous mixturesibd vs ibswhite blood cells granulocytes and agranulocytesdefine heterogenous mixturedefinition for protagonist and antagonistexamples of continuous spectrumdefine finite verbsbilateral symmetry definition biologywords that rhyme with stepsvoltmeter and ammeter differencemitosis vs meiosis differencesdifference between turtle & tortoisehow do you spell auntietonne vs metric tonneare algae autotrophs or heterotrophsmolarity vs densityprokaryotic transcription factorsis whipping cream and heavy cream the samekingdom archaebacteria and eubacteriaavenge vs revengedifferentiate between gymnosperms and angiospermsdifference between elastic and inelastic physicswhat is the difference between hypoxia and hypoxemiadefine enjambmentdifference between whisky and brandy2d heart echoconsumer and producer surplusdefine homopolymerabsorb vs adsorb