{"id":1708,"date":"2023-07-25T07:19:45","date_gmt":"2023-07-25T07:19:45","guid":{"rendered":"https:\/\/statorials.org\/pl\/produkt-kropkowy-ti-84\/"},"modified":"2023-07-25T07:19:45","modified_gmt":"2023-07-25T07:19:45","slug":"produkt-kropkowy-ti-84","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/produkt-kropkowy-ti-84\/","title":{"rendered":"Jak obliczy\u0107 iloczyn skalarny na kalkulatorze ti-84"},"content":{"rendered":"<p><\/p>\n<hr>\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;\">Mo\u017cemy u\u017cy\u0107 nast\u0119puj\u0105cej sk\u0142adni do obliczenia iloczynu skalarnego dw\u00f3ch wektor\u00f3w na kalkulatorze TI-84:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 17px;\"> <strong><span style=\"color: #3366ff;\">sum<\/span> ({2, 5, 6} <span style=\"color: #3366ff;\">*<\/span> {4, 3, 2})\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Poni\u017cszy przyk\u0142ad krok po kroku pokazuje, jak zastosowa\u0107 t\u0119 sk\u0142adni\u0119 w praktyce.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Przyk\u0142ad: Oblicz iloczyn skalarny na kalkulatorze TI-84<\/strong><\/span><\/h3>\n<p> Aby obliczy\u0107 iloczyn skalarny mi\u0119dzy dwoma wektorami, wykonaj nast\u0119puj\u0105ce kroki:<\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 1: Wprowad\u017a polecenie sum(.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Najpierw naci\u015bnij <span style=\"border: 1px solid black;\">2.<\/span> , nast\u0119pnie naci\u015bnij <span style=\"border: 1px solid black;\">STAT,<\/span> nast\u0119pnie przewi\u0144 do <span style=\"border: 1px solid black;\">MATH<\/span> i naci\u015bnij <span style=\"border: 1px solid black;\">sum\u0119<\/span> :<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-16827 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/point1-1.png\" alt=\"\" width=\"296\" height=\"253\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 2: Wprowad\u017a lewy nawias klamrowy.<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie naci\u015bnij <span style=\"border: 1px solid black;\">2.,<\/span> a nast\u0119pnie naci\u015bnij <span style=\"border: 1px solid black;\">(,<\/span> aby wprowadzi\u0107 pierwszy nawias klamrowy:<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-16828 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/point2-1.png\" alt=\"\" width=\"297\" height=\"260\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\"><strong>Krok 3: Wprowad\u017a dane<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Nast\u0119pnie wprowad\u017a nast\u0119puj\u0105ce warto\u015bci dla ka\u017cdego wektora:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Wektor a: 2, 5, 6<\/span><\/li>\n<li> <span style=\"color: #000000;\">Wektor b: 4, 3, 2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Upewnij si\u0119, \u017ce mi\u0119dzy dwoma wektorami znajduje si\u0119 znak mno\u017cenia, a koniec polecenia sum() zamknij prawym nawiasem. Nast\u0119pnie naci\u015bnij <span style=\"border: 1px solid black;\">ENTER<\/span> :<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-16829\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/point3-1.png\" alt=\"Iloczyn kropkowy na kalkulatorze TI-84\" width=\"304\" height=\"266\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Iloczyn skalarny okazuje si\u0119 wynosi\u0107 <strong>35<\/strong> . Odpowiada to warto\u015bci, kt\u00f3r\u0105 obliczyli\u015bmy r\u0119cznie.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Dodatkowe zasoby<\/strong><\/span><\/h3>\n<p> <a href=\"https:\/\/statorials.org\/pl\/jak-\u0142atwo-obliczyc-iloczyn-dote-w-programie-excel\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 iloczyn skalarny w programie Excel<\/a><br \/><a href=\"https:\/\/statorials.org\/pl\/kropka-arkusze-google-produktow\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 iloczyn skalarny w Arkuszach Google<\/a><br \/> <a href=\"https:\/\/statorials.org\/pl\/iloczyn-kropkowy-w-r\/\" target=\"_blank\" rel=\"noopener\">Jak obliczy\u0107 iloczyn skalarny w R<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>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: ab = za 1 * b 1 + za 2 * b 2 + za 3 [&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-1708","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - 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