{"id":1068,"date":"2023-07-27T18:49:04","date_gmt":"2023-07-27T18:49:04","guid":{"rendered":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/"},"modified":"2023-07-27T18:49:04","modified_gmt":"2023-07-27T18:49:04","slug":"kropka-arkusze-google-produktow","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/","title":{"rendered":"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w arkuszach google"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">W tym samouczku wyja\u015bniono, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Co to jest iloczyn skalarny?<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Maj\u0105c wektor <em>a<\/em> = [a <sub>1<\/sub> , a <sub>2<\/sub> , a <sub>3<\/sub> ] i wektor <em>b<\/em> = [b <sub>1<\/sub> , b <sub>2<\/sub> , b <sub>3<\/sub> ], <strong>iloczyn skalarny<\/strong> wektora a i wektora b, oznaczony <strong>ab<\/strong> , jest dany wzorem:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab<\/strong> = za <sub>1<\/sub> * b <sub>1<\/sub> + za <sub>2<\/sub> * b <sub>2<\/sub> + za <sub>3<\/sub> * b <sub>3<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad, je\u015bli <em>a<\/em> = [2, 5, 6] i <em>b<\/em> = [4, 3, 2], to iloczyn skalarny <em>a<\/em> i <em>b<\/em> b\u0119dzie r\u00f3wny:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab =<\/strong> 2*4 + 5*3 + 6*2<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>ab =<\/strong> 8 + 15 + 12<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>odb =<\/strong> 35<\/span><\/p>\n<p> <span style=\"color: #000000;\">Zasadniczo <strong>iloczyn skalarny<\/strong> jest sum\u0105 iloczyn\u00f3w odpowiednich wpis\u00f3w w dw\u00f3ch wektorach.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Jak znale\u017a\u0107 iloczyn kropkowy w Arkuszach Google<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Aby znale\u017a\u0107 iloczyn skalarny dw\u00f3ch wektor\u00f3w w Arkuszach Google, mo\u017cemy wykona\u0107 nast\u0119puj\u0105ce kroki:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Wprowad\u017a dane<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw wprowad\u017a warto\u015bci danych pierwszego wektora w jednej kolumnie, a warto\u015bci danych drugiego wektora w drugiej kolumnie:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11002 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/dotprodfeuilles1.png\" alt=\"\" width=\"385\" height=\"380\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Oblicz iloczyn skalarny.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby obliczy\u0107 iloczyn skalarny, mo\u017cemy u\u017cy\u0107 funkcji <strong>SUMPRODUCT()<\/strong> , kt\u00f3ra wykorzystuje nast\u0119puj\u0105c\u0105 sk\u0142adni\u0119:<\/span><\/p>\n<p style=\"text-align: center;\"> <span style=\"color: #000000;\"><strong>SUMPRODUKT(tabela1, [tabela2], \u2026)<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>tablica<\/strong> \u2013 pierwsza tablica lub zakres do pomno\u017cenia, a nast\u0119pnie dodania.<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>tablica2<\/strong> \u2013 druga tablica lub zakres do pomno\u017cenia, a nast\u0119pnie dodania.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017cszy obrazek pokazuje, jak u\u017cywa\u0107 tej funkcji do obliczania iloczynu skalarnego mi\u0119dzy tymi dwoma wektorami:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11003 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/dotprodfeuilles2.png\" alt=\"Produkt kropkowy w Arkuszach Google\" width=\"653\" height=\"394\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Daje to warto\u015b\u0107 <strong>35<\/strong> , kt\u00f3ra jest odpowiedzi\u0105, kt\u00f3r\u0105 otrzymali\u015bmy r\u0119cznie.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Nale\u017cy zauwa\u017cy\u0107, \u017ce funkcja <strong>SUMRRODUCT()<\/strong> dzia\u0142a dla wektor\u00f3w o dowolnej d\u0142ugo\u015bci. Na przyk\u0142ad mo\u017cemy u\u017cy\u0107 tej funkcji do obliczenia iloczynu skalarnego mi\u0119dzy dwoma wektorami o d\u0142ugo\u015bci 20:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-11005 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/dotprodfeuilles3.png\" alt=\"Formu\u0142a produktu kropkowego w Arkuszach Google\" width=\"658\" height=\"483\" srcset=\"\" sizes=\"auto, \"><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Potencjalne b\u0142\u0119dy w obliczaniu iloczynu skalarnego<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Funkcja <strong>SUMPRODUCT()<\/strong> zwr\u00f3ci <strong>#WARTO\u015a\u0106!<\/strong> b\u0142\u0105d, je\u015bli wektory nie maj\u0105 tej samej d\u0142ugo\u015bci.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Na przyk\u0142ad, je\u015bli pierwszy wektor ma d\u0142ugo\u015b\u0107 20, a drugi wektor<i> <\/i>ma d\u0142ugo\u015b\u0107 19, w\u00f3wczas formu\u0142a <strong>=SUMPRODUCT(A1:A20, B1:B19)<\/strong> zwr\u00f3ci b\u0142\u0105d.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Aby mo\u017cna by\u0142o obliczy\u0107 iloczyn skalarny, oba wektory musz\u0105 mie\u0107 t\u0119 sam\u0105 d\u0142ugo\u015b\u0107.<\/span><\/p>\n<p> <strong><span style=\"color: #000000;\">Powi\u0105zane:<\/span><\/strong> <a href=\"https:\/\/statorials.org\/pl\/jak-\u0142atwo-obliczyc-iloczyn-dote-w-programie-excel\/\" target=\"_blank\" rel=\"noopener noreferrer\">Jak obliczy\u0107 iloczyn skalarny w programie Excel<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>W tym samouczku wyja\u015bniono, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google. Co to jest iloczyn skalarny? Maj\u0105c wektor a = [a 1 , a 2 , a 3 ] i wektor b = [b 1 , b 2 , b 3 ], iloczyn skalarny wektora a i wektora b, oznaczony ab , jest dany wzorem: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-1068","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak \u0142atwo obliczy\u0107 iloczyn skalarny w Arkuszach Google<\/title>\n<meta name=\"description\" content=\"Proste wyja\u015bnienie, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google, z przyk\u0142adem.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w Arkuszach Google\" \/>\n<meta property=\"og:description\" content=\"Proste wyja\u015bnienie, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google, z przyk\u0142adem.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-27T18:49:04+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/dotprodfeuilles1.png\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\",\"url\":\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\",\"name\":\"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w Arkuszach Google\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-27T18:49:04+00:00\",\"dateModified\":\"2023-07-27T18:49:04+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"Proste wyja\u015bnienie, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google, z przyk\u0142adem.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w arkuszach google\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej\",\"sameAs\":[\"https:\/\/statorials.org\/pl\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w Arkuszach Google","description":"Proste wyja\u015bnienie, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google, z przyk\u0142adem.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/","og_locale":"pl_PL","og_type":"article","og_title":"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w Arkuszach Google","og_description":"Proste wyja\u015bnienie, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google, z przyk\u0142adem.","og_url":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/","og_site_name":"Statorials","article_published_time":"2023-07-27T18:49:04+00:00","og_image":[{"url":"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/dotprodfeuilles1.png"}],"author":"Benjamin Anderson","twitter_card":"summary_large_image","twitter_misc":{"Napisane przez":"Benjamin Anderson","Szacowany czas czytania":"2 minuty"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/","url":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/","name":"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w Arkuszach Google","isPartOf":{"@id":"https:\/\/statorials.org\/pl\/#website"},"datePublished":"2023-07-27T18:49:04+00:00","dateModified":"2023-07-27T18:49:04+00:00","author":{"@id":"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965"},"description":"Proste wyja\u015bnienie, jak obliczy\u0107 iloczyn skalarny w Arkuszach Google, z przyk\u0142adem.","breadcrumb":{"@id":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/#breadcrumb"},"inLanguage":"pl-PL","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Dom","item":"https:\/\/statorials.org\/pl\/"},{"@type":"ListItem","position":2,"name":"Jak \u0142atwo obliczy\u0107 iloczyn skalarny w arkuszach google"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/pl\/#website","url":"https:\/\/statorials.org\/pl\/","name":"Statorials","description":"Tw\u00f3j przewodnik po kompetencjach statystycznych!","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/pl\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"pl-PL"},{"@type":"Person","@id":"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965","name":"Benjamin Anderson","image":{"@type":"ImageObject","inLanguage":"pl-PL","@id":"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg","caption":"Benjamin Anderson"},"description":"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. Dzi\u0119ki bogatemu do\u015bwiadczeniu i wiedzy specjalistycznej w dziedzinie statystyki ch\u0119tnie dziel\u0119 si\u0119 swoj\u0105 wiedz\u0105, aby wzmocni\u0107 pozycj\u0119 uczni\u00f3w za po\u015brednictwem Statorials. Wiedzie\u0107 wi\u0119cej","sameAs":["https:\/\/statorials.org\/pl"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/1068","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/comments?post=1068"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/posts\/1068\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/media?parent=1068"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/categories?post=1068"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/pl\/wp-json\/wp\/v2\/tags?post=1068"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}