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 Reply

Related pages

difference between lifi and wifiimperialism characteristicspermitivity of free spacehow are the inner planets differentcharacteristics of alpha beta and gamma raysexample of anastropheleucoderma or vitiligodefine simple distillationsnuggle definitiondelusions vs hallucinationdefinition of suspension chemistryb6 vs b12molecular formula for maltosereflecting telescope vs refractingmeaning of anecdoteshomonym and homophone differencemitosis in plant cells vs animal cellsdefine polysemywhat is the difference between aisle and islesliding friction definition physicsdefine conductor and insulatormonozygotic and dizygotic twinswhat is the difference between raw and pure honeyleast count of vernier calliperswhat is the difference between monozygotic and dizygotic twinsdefinition of pteridophyteschamfered edgedifference between a covalent and ionic bonddifference between static friction and sliding frictionthermosetting plastics propertiesexample of an internal rhymethyroid hypo vs hypermaid of honor matron of honor differencefructose structural formulawhat are spermatogenesis and oogenesischemical properties of cycloalkanesbaking soda bicarbonate of soda same thingdifference between hypoglycemia and hyperglycemiawhat is the difference between melting and freezingdiagram of a longitudinal waveconscious mind subconscious minddefinition of pure substance and mixturedifference between values and moralslayed laiddefinition of monocotyledon and dicotyledonverisimilitude in literatureamoral meaningsanitary fittings definitionprose and verse definitionexample of diamante poemsrelationship between hardness and toughnessenglish mastiff weightintensive pronounwhat is closed syllablerelay or contactorbarley flour vs wheat flourwhat is the difference between diabetes mellitus and diabetes insipiduscarpe diem poemthe definition of flat characterenquiry inquiry differencecompare autotrophs and heterotrophstensile vs yield strengthhomophone vs homographmultinational corporations meaningdifference alligators and crocodilescollenchyma parenchyma sclerenchymaacceleration triangledefinition regular polygonwhat is the difference between aliphatic and aromatic hydrocarbonscbt dbt therapydifference between zygote and foetusare homologous chromosomes identicalbonding in sucrosemoral of cinderella storyunpolarised light definitionsimilarities between kwashiorkor and marasmuscompare viber and skypecharacteristics of infatuationwhat is the difference between workshop and seminardeterminers adjectivesspices condiments and seasoningsdifference between bipolar and schizophrenia symptoms