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


is jupiter an inner or outer planetare orchids monocots or dicotsadjectives of numbersdeoxyribose moleculedifferentiate between self and cross pollinationhow to write a iambic pentameter poemexamples of consonants soundscoefficient of friction meaningwhat is the difference between intermolecular and intramolecular forceswhat is the difference between polar and nonpolar bondsmadam in french translationcolorimeter spectrophotometerwhat is the difference between the purines and the pyrimidineschemical formula for nitrate iondifference between teflon and ptfedifference between a lab and a retrieverrelation between transmittance and absorbancesleep apnea vs insomniawhat are the physical properties of alkanesenjambment poetry exampleswhat is the difference between epistemology and ontologywhat is the difference between copd and emphysemapoem refraindifference between fever blister and cold sorevibration oscillationdmitri mendeleev definitionribose fischerearl baron dukeexample of hamartiaconcrete vs abstract nounsdefinition of isosmoticdefine affected vs effecteddifference between black and english walnutsdelusion hallucinationdefine vernierdifference between noun clause and noun phrasefunction of radicle in seeddifference between a moose and a cariboudistinguish between prokaryotes and eukaryoteswhat is the difference between action verbs and linking verbsdefinition of transnational strategydistinguish between autotrophic and heterotrophic nutritionstoma guard cellsdifferences between solute and solventexplanation of alliterationdifference between epiglottis and uvulasignificance of harlem renaissancewhat is the difference between liking someone and loving someonezener breakdown mechanismhow to write ekphrastic poetrysyntactic parallelismguanine definitionwhat is satire in dramawhats foreshadowingpixie fairieswhat is the difference between infinitive and gerundintrovert qualitiesdefine monologueswhat subatomic particle is involved in chemical reactionswhat is the definition of rhymebalanced and unbalanced force definitionwhat is the difference between symbolism and allegoryflagella vs ciliadifference between hurricane cyclone and tornadoexplain the process of transcription in prokaryotesthe meaning of paildifference between green onions and scallionspride dictionary definitiondefine anthropomorphismwhat is the main difference between gymnosperms and angiosperms