{"id":10382,"date":"2025-01-23T06:15:10","date_gmt":"2025-01-23T03:15:10","guid":{"rendered":"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/"},"modified":"2025-01-23T06:15:10","modified_gmt":"2025-01-23T03:15:10","slug":"vektor-cikarma-islemi-detayli-anlatim","status":"publish","type":"post","link":"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/","title":{"rendered":"Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m"},"content":{"rendered":"<p><body><\/p>\n<p>Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m<\/p>\n<p>Merhaba! Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele alaca\u011f\u0131z. \u00d6ncelikle vekt\u00f6r kavram\u0131n\u0131 k\u0131saca hat\u0131rlayal\u0131m.  Vekt\u00f6rler, b\u00fcy\u00fckl\u00fck ve y\u00f6n\u00fc olan niceliklerdir.  Bunlar\u0131 genellikle oklar ile temsil ederiz.  \u00d6rne\u011fin, h\u0131z, kuvvet ve ivme gibi fiziksel nicelikler vekt\u00f6rlerle ifade edilir.  Ancak vekt\u00f6r kavram\u0131 fizikle s\u0131n\u0131rl\u0131 kalmaz; matematik, bilgisayar bilimleri ve daha bir\u00e7ok alanda kullan\u0131l\u0131r.<\/p>\n<h2>Vekt\u00f6r \u00c7\u0131karma Nas\u0131l Yap\u0131l\u0131r?<\/h2>\n<p>\u0130ki vekt\u00f6r\u00fc \u00e7\u0131karma i\u015flemi, asl\u0131nda bir vekt\u00f6r toplama i\u015flemine indirgenir.  \u0130lk vekt\u00f6r\u00fc, ikinci vekt\u00f6r\u00fcn tersini ile toplar\u0131z. Yani, <strong>a &#8211; b = a + (-b)<\/strong> \u015feklindedir.  Burada -b, b vekt\u00f6r\u00fcn\u00fcn y\u00f6n\u00fc tersine \u00e7evrilmi\u015f halidir.  Bu, b vekt\u00f6r\u00fcn\u00fcn hem b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc hem de y\u00f6n\u00fcn\u00fc de\u011fi\u015ftirmemiz gerekti\u011fi anlam\u0131na gelir.  Daha a\u00e7\u0131klay\u0131c\u0131 olmak gerekirse,  b vekt\u00f6r\u00fcn\u00fcn her bile\u015fenin i\u015faretini de\u011fi\u015ftiririz ve bu yeni vekt\u00f6r\u00fc a vekt\u00f6r\u00fc ile toplar\u0131z. <\/p>\n<p>\u00d6rne\u011fin, a = (3, 2) ve b = (1, 1) vekt\u00f6rlerini ele alal\u0131m.  b vekt\u00f6r\u00fcn\u00fcn tersi -b = (-1, -1) olur.  \u015eimdi a ve -b vekt\u00f6rlerini toplayal\u0131m: a + (-b) = (3, 2) + (-1, -1) = (3 &#8211; 1, 2 &#8211; 1) = (2, 1).  Dolay\u0131s\u0131yla, a &#8211; b = (2, 1) sonucunu elde ederiz.  Bu i\u015flem, geometrik olarak da d\u00fc\u015f\u00fcn\u00fclebilir.  a vekt\u00f6r\u00fcnden b vekt\u00f6r\u00fcn\u00fc \u00e7\u0131karmak, a vekt\u00f6r\u00fcn\u00fcn ba\u015flang\u0131\u00e7 noktas\u0131ndan b vekt\u00f6r\u00fcn\u00fcn ucuna bir vekt\u00f6r \u00e7izmek anlam\u0131na gelir.<\/p>\n<h3>\u00d6rnekler ve G\u00f6rseller<\/h3>\n<p>Farkl\u0131 boyutlardaki vekt\u00f6rler i\u00e7in de benzer bir i\u015flem uygulan\u0131r. \u00dc\u00e7 boyutlu vekt\u00f6rlerde, her bir bile\u015fen i\u00e7in ayn\u0131 \u00e7\u0131karma i\u015flemini yapar\u0131z.  \u00d6rne\u011fin,  a = (2, 4, 6) ve b = (1, 2, 3) ise, a &#8211; b = (2-1, 4-2, 6-3) = (1, 2, 3) olur. <a href=\"https:\/\/dev.to\/bazengdev\/subtracting-vectors-13jk\">\u0130ngilizce kaynakta bulunan g\u00f6rselleri inceleyerek<\/a> daha iyi anlayabilirsiniz.  Bu g\u00f6rseller, vekt\u00f6r \u00e7\u0131karma i\u015flemini daha somut bir \u015fekilde g\u00f6stermektedir.<\/p>\n<h2>Vekt\u00f6r \u00c7\u0131karma ve Uygulamalar\u0131<\/h2>\n<p>Vekt\u00f6r \u00e7\u0131karma,  fizikte kuvvetlerin bile\u015fkesinin hesaplanmas\u0131, bilgisayar grafiklerinde nesnelerin konumland\u0131r\u0131lmas\u0131 ve  makine \u00f6\u011frenmesinde vekt\u00f6r uzaylar\u0131nda i\u015flemler yapmak gibi bir\u00e7ok alanda kullan\u0131l\u0131r.  \u00d6rne\u011fin, bir u\u00e7a\u011f\u0131n h\u0131z\u0131 ve r\u00fczgar\u0131n h\u0131z\u0131 bilindi\u011finde, u\u00e7a\u011f\u0131n net h\u0131z\u0131 vekt\u00f6r \u00e7\u0131karma i\u015flemi ile bulunabilir.  <a href=\"https:\/\/fatihsoysal.com\">Kendi web sitemde<\/a> vekt\u00f6rlerle ilgili daha fazla bilgi bulabilirsiniz.<\/p>\n<p>Sonu\u00e7 olarak, vekt\u00f6r \u00e7\u0131karma i\u015flemi, vekt\u00f6r cebirinin temel bir par\u00e7as\u0131d\u0131r ve bir\u00e7ok uygulama alan\u0131na sahiptir.  Bu makalede anlatt\u0131\u011f\u0131m y\u00f6ntemleri kullanarak,  farkl\u0131 vekt\u00f6rleri kolayca \u00e7\u0131karabilirsiniz.  Umar\u0131m bu makale size yard\u0131mc\u0131 olmu\u015ftur!<\/p>\n<p><strong>#Etiketler:<\/strong> vekt\u00f6r \u00e7\u0131karma, vekt\u00f6r i\u015flemleri, vekt\u00f6r toplama, lineer cebir, matematik, geometri, vekt\u00f6r uzay\u0131, vekt\u00f6r hesaplama<\/p>\n<p><\/body><br \/>\n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m Merhaba! Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele&hellip;","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"csco_page_header_type":"","csco_page_load_nextpost":"","csco_page_subscribe_form":"","csco_page_contact_form":"","footnotes":""},"categories":[1],"tags":[],"class_list":{"0":"post-10382","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-genel","7":"cs-entry","8":"cs-video-wrap"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v20.5 (Yoast SEO v25.3.1) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m<\/title>\n<meta name=\"description\" content=\"Merhaba! Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele alaca\u011f\u0131z. \u00d6ncelikle vekt\u00f6r kavram\u0131n\u0131 k\u0131saca hat\u0131rlayal\u0131m. Vekt\u00f6rler, b\u00fcy\u00fckl\u00fck ve y\u00f6n\u00fc olan niceliklerdir. Bunlar\u0131 genellikle oklar ile temsil ederiz. \u00d6rne\u011fin, h\u0131z, kuvvet ve ivme gibi fiziksel nicelikler vekt\u00f6rlerle ifade edilir. Ancak vekt\u00f6r kavram\u0131 fizikle s\u0131n\u0131rl\u0131 kalmaz; matematik, bilgisayar bilimleri ve daha bir\u00e7ok alanda kullan\u0131l\u0131r.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m\" \/>\n<meta property=\"og:description\" content=\"Merhaba! Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele alaca\u011f\u0131z. \u00d6ncelikle vekt\u00f6r kavram\u0131n\u0131 k\u0131saca hat\u0131rlayal\u0131m. Vekt\u00f6rler, b\u00fcy\u00fckl\u00fck ve y\u00f6n\u00fc olan niceliklerdir. Bunlar\u0131 genellikle oklar ile temsil ederiz. \u00d6rne\u011fin, h\u0131z, kuvvet ve ivme gibi fiziksel nicelikler vekt\u00f6rlerle ifade edilir. Ancak vekt\u00f6r kavram\u0131 fizikle s\u0131n\u0131rl\u0131 kalmaz; matematik, bilgisayar bilimleri ve daha bir\u00e7ok alanda kullan\u0131l\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/\" \/>\n<meta property=\"og:site_name\" content=\"Kodlar\u0131n Gizemli D\u00fcnyas\u0131\" \/>\n<meta property=\"article:published_time\" content=\"2025-01-23T03:15:10+00:00\" \/>\n<meta name=\"author\" content=\"Fatih Soysal\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Fatih Soysal\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/\"},\"author\":{\"name\":\"Fatih Soysal\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"headline\":\"Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m\",\"datePublished\":\"2025-01-23T03:15:10+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/\"},\"wordCount\":490,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#\/schema\/person\/002a254750921dcfd568a99e48240dd1\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/#respond\"]}],\"copyrightYear\":\"2025\",\"copyrightHolder\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#organization\"}},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/\",\"url\":\"https:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/\",\"name\":\"Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m\",\"isPartOf\":{\"@id\":\"https:\/\/fatihsoysal.com\/blog\/#website\"},\"datePublished\":\"2025-01-23T03:15:10+00:00\",\"description\":\"Merhaba! Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele alaca\u011f\u0131z. \u00d6ncelikle vekt\u00f6r kavram\u0131n\u0131 k\u0131saca hat\u0131rlayal\u0131m. Vekt\u00f6rler, b\u00fcy\u00fckl\u00fck ve y\u00f6n\u00fc olan niceliklerdir. Bunlar\u0131 genellikle oklar ile temsil ederiz. \u00d6rne\u011fin, h\u0131z, kuvvet ve ivme gibi fiziksel nicelikler vekt\u00f6rlerle ifade edilir. 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Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele alaca\u011f\u0131z. \u00d6ncelikle vekt\u00f6r kavram\u0131n\u0131 k\u0131saca hat\u0131rlayal\u0131m. Vekt\u00f6rler, b\u00fcy\u00fckl\u00fck ve y\u00f6n\u00fc olan niceliklerdir. Bunlar\u0131 genellikle oklar ile temsil ederiz. \u00d6rne\u011fin, h\u0131z, kuvvet ve ivme gibi fiziksel nicelikler vekt\u00f6rlerle ifade edilir. Ancak vekt\u00f6r kavram\u0131 fizikle s\u0131n\u0131rl\u0131 kalmaz; matematik, bilgisayar bilimleri ve daha bir\u00e7ok alanda kullan\u0131l\u0131r.","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:\/\/fatihsoysal.com\/blog\/vektor-cikarma-islemi-detayli-anlatim\/","og_locale":"tr_TR","og_type":"article","og_title":"Vekt\u00f6r \u00c7\u0131karma \u0130\u015flemi: Detayl\u0131 Anlat\u0131m","og_description":"Merhaba! Fatih Soysal olarak, bu makalede vekt\u00f6r \u00e7\u0131karma i\u015flemini detayl\u0131 bir \u015fekilde ele alaca\u011f\u0131z. \u00d6ncelikle vekt\u00f6r kavram\u0131n\u0131 k\u0131saca hat\u0131rlayal\u0131m. Vekt\u00f6rler, b\u00fcy\u00fckl\u00fck ve y\u00f6n\u00fc olan niceliklerdir. Bunlar\u0131 genellikle oklar ile temsil ederiz. \u00d6rne\u011fin, h\u0131z, kuvvet ve ivme gibi fiziksel nicelikler vekt\u00f6rlerle ifade edilir. 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