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vector operator wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 see also 2 references 3 further reading toggle the table of contents vector operator 4 languages català español shqip 中文 edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia differential operator used in vector calculus a vector operator is a differential operator used in vector calculus 1 vector operators include gradient is a vector operator that operates on a scalar field producing a vector field divergence is a vector operator that operates on a vector field producing a scalar field curl is a vector operator that operates on a vector field producing a vector field defined in terms of del grad div curl displaystyle begin aligned operatorname grad equiv nabla operatorname div equiv nabla cdot operatorname curl equiv nabla times end aligned the laplacian operates on a scalar field producing a scalar field 2 div grad displaystyle nabla 2 equiv operatorname div operatorname grad equiv nabla cdot nabla vector operators must always come right before the scalar field or vector field on which they operate in order to produce a result e g f displaystyle nabla f yields the gradient of f but f displaystyle f nabla is just another vector operator which is not operating on anything a vector operator can operate on another vector operator to produce a compound vector operator as seen above in the case of the laplacian see also edit del d alembert operator references edit 12 2 vector operators physics libretexts 2020 05 09 retrieved 2025 05 14 further reading edit h m schey 1996 div grad curl and all that an informal text on vector calculus isbn 0 393 96997 5 retrieved from https en wikipedia org w index php title vector_operator oldid 1318073391 category vector calculus hidden categories articles with short description short description matches wikidata this page was last edited on 21 october 2025 at 19 33 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents vector operator 4 languages add topic