{"id":32,"date":"2026-10-03T11:03:03","date_gmt":"2026-10-03T10:03:03","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/2b-vektor-arasi-acisi\/"},"modified":"2026-10-03T11:03:03","modified_gmt":"2026-10-03T10:03:03","slug":"2b-vektor-arasi-acisi","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/2b-vektor-arasi-acisi\/","title":{"rendered":"2B Vekt\u00f6rler Aras\u0131 A\u00e7\u0131 Hesaplama"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">\u0130ki 2D Vekt\u00f6r Aras\u0131ndaki A\u00e7\u0131y\u0131 Hesaplay\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"32\" data-favorite-title=\"2B Vekt\u00f6rler Aras\u0131 A\u00e7\u0131\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/2b-vektor-arasi-acisi\/\" data-favorite-excerpt=\"\u0130ki vekt\u00f6r\u00fcn X ve Y bile\u015fenlerini girerek aralar\u0131ndaki a\u00e7\u0131y\u0131 derece cinsinden bulun. Hesaplay\u0131c\u0131, nokta \u00e7arp\u0131m form\u00fcl\u00fcn\u00fc kullan\u0131r ve fizik, geometri ile bilgisayar grafiklerinde kullan\u0131\u015fl\u0131d\u0131r.\" aria-label=\"Favorilere ekle\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/tr\/matematik\/2b-vektor-arasi-acisi\/\" method=\"POST\" class=\"calculator\" id=\"calculator-32\" data-post=\"32\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">V1 Vekt\u00f6r\u00fc - X<\/label><input type=\"number\" name=\"v1_vektr_x\" id=\"field-1\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">V1 Vekt\u00f6r\u00fc - Y<\/label><input type=\"number\" name=\"v1_vektr_y\" id=\"field-2\" placeholder=\"0\" step=\"1\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">V2 Vekt\u00f6r\u00fc - X<\/label><input type=\"number\" name=\"v2_vektr_x\" id=\"field-3\" placeholder=\"0\" step=\"1\" value=\"0\"\/><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">V2 Vekt\u00f6r\u00fc - Y<\/label><input type=\"number\" name=\"v2_vektr_y\" id=\"field-4\" placeholder=\"1\" step=\"1\" value=\"1\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"32\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Sonu\u00e7lar\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Vekt\u00f6rler aras\u0131ndaki a\u00e7\u0131 (\u00b0)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Yorum b\u0131rak<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"32\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Be\u011fendim <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Faydal\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Kafam kar\u0131\u015ft\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Hatal\u0131 <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>\u0130ki 2B Vekt\u00f6r Aras\u0131ndaki A\u00e7\u0131 Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\theta = \\cos^{-1}\\left( \\frac{\\vec{A} \\cdot \\vec{B}}{|\\vec{A}| \\, |\\vec{B}|} \\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Burada:<\/strong><\/p>\n<ul>\n<li>\\(\\vec{A} \\cdot \\vec{B} = A_x B_x + A_y B_y\\) \u2014 iki vekt\u00f6r\u00fcn nokta \u00e7arp\u0131m\u0131 (skaler \u00e7arp\u0131m)<\/li>\n<li>\\(|\\vec{A}| = \\sqrt{A_x^2 + A_y^2}\\) \u2014 \\(\\vec{A}\\) vekt\u00f6r\u00fcn\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc (uzunlu\u011fu)<\/li>\n<li>\\(|\\vec{B}| = \\sqrt{B_x^2 + B_y^2}\\) \u2014 \\(\\vec{B}\\) vekt\u00f6r\u00fcn\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc (uzunlu\u011fu)<\/li>\n<li>\\(\\theta\\) \u2014 iki vekt\u00f6r aras\u0131ndaki a\u00e7\u0131<\/li>\n<\/ul>\n<p>Form\u00fcl, nokta \u00e7arp\u0131m\u0131n\u0131n geometrik tan\u0131m\u0131ndan gelir: \\(\\vec{A} \\cdot \\vec{B} = |\\vec{A}| |\\vec{B}| \\cos\\theta\\). Bu e\u015fitli\u011fi \\(\\theta\\) i\u00e7in \u00e7\u00f6zd\u00fc\u011f\u00fcm\u00fczde yukar\u0131daki ifade elde edilir. \\(\\cos^{-1}\\) i\u015fleminin sonucu radyan cinsindendir; \\(\\frac{180}{\\pi}\\) ile \u00e7arp\u0131larak dereceye d\u00f6n\u00fc\u015ft\u00fcr\u00fcl\u00fcr \u2014 bu hesaplay\u0131c\u0131 bu d\u00f6n\u00fc\u015f\u00fcm\u00fc sizin i\u00e7in yapar ve cevab\u0131 derece cinsinden verir.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>\u0130ki 2B Vekt\u00f6r Aras\u0131ndaki A\u00e7\u0131 \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\(\\vec{V_1} = (1, 0)\\) ve \\(\\vec{V_2} = (0, 1)\\) vekt\u00f6rleri aras\u0131ndaki a\u00e7\u0131y\u0131 bulal\u0131m.<\/p>\n<p>\\[ \\vec{V_1} \\cdot \\vec{V_2} = (1)(0) + (0)(1) = 0 \\]<\/p>\n<p>\\[ |\\vec{V_1}| = \\sqrt{1^2 + 0^2} = 1, \\qquad |\\vec{V_2}| = \\sqrt{0^2 + 1^2} = 1 \\]<\/p>\n<p>\\[ \\theta = \\cos^{-1}\\left( \\frac{0}{1 \\cdot 1} \\right) = \\cos^{-1}(0) = 90\u00b0 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> iki vekt\u00f6r aras\u0131ndaki a\u00e7\u0131 90\u00b0'dir. Vekt\u00f6rler dik ba\u015f\u0131na durur; bu da X ve Y eksenleri boyunca uzanan birim vekt\u00f6rlerden tam olarak beklenen sonu\u00e7tur.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplay\u0131c\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>\u0130lk vekt\u00f6r\u00fcn X bile\u015fenini <strong>Vekt\u00f6r V1 - X<\/strong> alan\u0131na girin.<\/li>\n<li>\u0130lk vekt\u00f6r\u00fcn Y bile\u015fenini <strong>Vekt\u00f6r V1 - Y<\/strong> alan\u0131na girin.<\/li>\n<li>\u0130kinci vekt\u00f6r\u00fcn X bile\u015fenini <strong>Vekt\u00f6r V2 - X<\/strong> alan\u0131na girin.<\/li>\n<li>\u0130kinci vekt\u00f6r\u00fcn Y bile\u015fenini <strong>Vekt\u00f6r V2 - Y<\/strong> alan\u0131na girin.<\/li>\n<li><strong>Vekt\u00f6rler aras\u0131 a\u00e7\u0131 (\u00b0)<\/strong> sonucunu okuyun. Cevap derece cinsinden, \u00fc\u00e7 ondal\u0131k basama\u011fa yuvarlanm\u0131\u015f olarak verilir.<\/li>\n<\/ol>\n<p>Pozitif ve negatif de\u011ferlerin yan\u0131 s\u0131ra ondal\u0131k say\u0131lar da kabul edilir. Vekt\u00f6rleri \u00f6nceden birim vekt\u00f6re d\u00f6n\u00fc\u015ft\u00fcrmenize gerek yoktur \u2014 form\u00fcl b\u00fcy\u00fckl\u00fcklere b\u00f6ld\u00fc\u011f\u00fc i\u00e7in vekt\u00f6r\u00fcn uzunlu\u011fu ne olursa olsun a\u00e7\u0131 ayn\u0131 kal\u0131r.<\/p>\n<h2>\u0130ki Vekt\u00f6r Aras\u0131ndaki A\u00e7\u0131 Nedir?<\/h2>\n<p>\u0130ki boyutta bir \\(\\vec{A} = (A_x, A_y)\\) vekt\u00f6r\u00fcn\u00fcn hem uzunlu\u011fu hem de y\u00f6n\u00fc vard\u0131r. \u0130ki vekt\u00f6r\u00fc ayn\u0131 noktadan ba\u015flayacak \u015fekilde yerle\u015ftirdi\u011finizde, aralar\u0131ndaki a\u00e7\u0131 y\u00f6nlerinin birbirinden ne kadar ayr\u0131k oldu\u011funu \u00f6l\u00e7er. Bu a\u00e7\u0131 daima 0\u00b0 ile 180\u00b0 aras\u0131ndad\u0131r: 0\u00b0 vekt\u00f6rlerin ayn\u0131 y\u00f6ne bakt\u0131\u011f\u0131, 90\u00b0 dik ba\u015f\u0131na durduklar\u0131, 180\u00b0 ise tam ters y\u00f6nlere bakt\u0131klar\u0131 anlam\u0131na gelir.<\/p>\n<p>Bu a\u00e7\u0131y\u0131 hesaplaman\u0131n anahtar\u0131 <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/2b-vektor-skaler-carpim\/\">nokta \u00e7arp\u0131m\u0131d\u0131r<\/a>. Nokta \u00e7arp\u0131m\u0131, iki vekt\u00f6r\u00fcn y\u00f6nelimlerinin ne kadar \u00f6rt\u00fc\u015ft\u00fc\u011f\u00fcn\u00fc \u00f6l\u00e7er: b\u00fcy\u00fck bir pozitif nokta \u00e7arp\u0131m\u0131 vekt\u00f6rlerin kabaca ayn\u0131 y\u00f6ne bakt\u0131\u011f\u0131, s\u0131f\u0131r dik olduklar\u0131, negatif de\u011fer ise a\u00e7\u0131n\u0131n geni\u015f (obtuse) oldu\u011fu anlam\u0131na gelir. Nokta \u00e7arp\u0131m\u0131n\u0131 b\u00fcy\u00fckl\u00fcklerin \u00e7arp\u0131m\u0131na b\u00f6lmek \\(\\cos\\theta\\) de\u011ferini verir; arkkosin\u00fcs ise a\u00e7\u0131n\u0131n kendisini geri getirir.<\/p>\n<p>Vekt\u00f6rler aras\u0131ndaki a\u00e7\u0131y\u0131 bilmek bir\u00e7ok pratik durumda \u00f6nemlidir. Fizikte kuvvetleri bile\u015fenlerine ay\u0131rman\u0131za ve i\u015f hesaplamalar\u0131n\u0131za olanak tan\u0131r; \u00e7\u00fcnk\u00fc i\u015f, \\(F \\cdot d \\cdot \\cos\\theta\\) e\u015fitli\u011fine e\u015fittir. Bilgisayar grafiklerinde ve oyun geli\u015ftirmede g\u00f6r\u00fc\u015f alan\u0131 (field-of-view) kontrollerinde, \u0131\u015f\u0131kland\u0131rma hesaplar\u0131nda ve nesneleri hedeflere do\u011fru d\u00f6nd\u00fcrmede kullan\u0131l\u0131r. Navigasyon ve robotikte ise bir sisteme istenen y\u00f6ne d\u00f6nebilmesi i\u00e7in ne kadar d\u00f6nmesi gerekti\u011fini s\u00f6yler.<\/p>\n<p>Vekt\u00f6rlerin kendisiyle \u00e7al\u0131\u015fmak i\u00e7in <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/2d-vektor-buyuklugu\/\">2B Vekt\u00f6r B\u00fcy\u00fckl\u00fc\u011f\u00fc<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/2b-vektor-toplama\/\">2B Vekt\u00f6r Toplam\u0131<\/a> hesaplay\u0131c\u0131lar\u0131n\u0131 da faydal\u0131 bulabilirsiniz.<\/p>\n<h2>Sonucun Yorumlanmas\u0131<\/h2>\n<p>Hesaplay\u0131c\u0131 her zaman 0\u00b0 ile 180\u00b0 aras\u0131ndaki k\u00fc\u00e7\u00fck a\u00e7\u0131y\u0131 d\u00f6nd\u00fcr\u00fcr. Bu, al\u0131\u015f\u0131lm\u0131\u015f \"vekt\u00f6rler aras\u0131 a\u00e7\u0131\" tan\u0131m\u0131d\u0131r ve hangi vekt\u00f6r\u00fcn di\u011ferine g\u00f6re saat y\u00f6n\u00fcnde ya da saat y\u00f6n\u00fcn\u00fcn tersine d\u00f6nd\u00fcr\u00fclm\u00fc\u015f oldu\u011funu s\u00f6ylemez. \u0130\u015faretli bir a\u00e7\u0131ya ihtiyac\u0131n\u0131z varsa (\u00f6rne\u011fin bir oyunda hangi y\u00f6ne d\u00f6nece\u011fe karar vermek i\u00e7in), \\(A_x B_y - A_y B_x\\) vekt\u00f6rel \u00e7arp\u0131m\u0131n\u0131 da hesaplay\u0131n: i\u015fareti size d\u00f6n\u00fc\u015f y\u00f6n\u00fcn\u00fc s\u00f6yleyecektir.<\/p>\n<p>Girdilerinizi sa\u011flama almak i\u00e7in faydal\u0131 baz\u0131 \u00f6zel durumlar:<\/p>\n<table>\n<thead>\n<tr>\n<th>Vekt\u00f6rler<\/th>\n<th>A\u00e7\u0131<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Ayn\u0131 y\u00f6n (paralel)<\/td>\n<td>0\u00b0<\/td>\n<\/tr>\n<tr>\n<td>Dik (nokta \u00e7arp\u0131m\u0131 = 0)<\/td>\n<td>90\u00b0<\/td>\n<\/tr>\n<tr>\n<td>Ters y\u00f6nler<\/td>\n<td>180\u00b0<\/td>\n<\/tr>\n<tr>\n<td>\u00d6zde\u015f vekt\u00f6rler<\/td>\n<td>0\u00b0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>S\u0131n\u0131rlamalar ve \u0130pu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>S\u0131f\u0131r vekt\u00f6rler:<\/strong> vekt\u00f6rlerden herhangi biri \\((0, 0)\\) ise y\u00f6n\u00fc tan\u0131ms\u0131zd\u0131r. Hesaplay\u0131c\u0131 bu durumda 0 d\u00f6nd\u00fcr\u00fcr; ancak matematiksel olarak a\u00e7\u0131 mevcut de\u011fildir.<\/li>\n<li><strong>Yuvarlama:<\/strong> kayan nokta aritmeti\u011fi nedeniyle, \\(\\cos^{-1}\\) i\u00e7ine giren 1'e veya -1'e \u00e7ok yak\u0131n de\u011ferler k\u00fc\u00e7\u00fck hatalara yol a\u00e7abilir; sonu\u00e7 \u00fc\u00e7 ondal\u0131k basama\u011fa yuvarlan\u0131r.<\/li>\n<li><strong>Birimler:<\/strong> sonu\u00e7 her zaman derece cinsindendir. Radyana d\u00f6n\u00fc\u015ft\u00fcrmek i\u00e7in \\(\\frac{\\pi}{180}\\) ile \u00e7arp\u0131n.<\/li>\n<li><strong>Y\u00f6n \u00f6nemli de\u011fildir:<\/strong> V1 ile V2'nin yerini de\u011fi\u015ftirmek ayn\u0131 a\u00e7\u0131y\u0131 verir; \u00e7\u00fcnk\u00fc nokta \u00e7arp\u0131m\u0131 de\u011fi\u015fmelidir.<\/li>\n<li><strong>\u00d6l\u00e7ek de\u011fi\u015fmezli\u011fi:<\/strong> vekt\u00f6rlerden birini pozitif bir say\u0131yla \u00e7arpmak a\u00e7\u0131y\u0131 de\u011fi\u015ftirmez; \u00e7\u00fcnk\u00fc b\u00fcy\u00fckl\u00fckler birbirini g\u00f6t\u00fcr\u00fcr.<\/li>\n<\/ul>\n<p>Bir d\u00fczlem yerine \u00fc\u00e7 boyutla \u00e7al\u0131\u015f\u0131yorsan\u0131z ayn\u0131 nokta \u00e7arp\u0131m\u0131 form\u00fcl\u00fc ge\u00e7erlidir \u2014 <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/3b-vektor-skaler-carpim\/\">3B Vekt\u00f6r Skaler \u00c7arp\u0131m\u0131<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/3b-vektor-buyuklugu\/\">3B Vekt\u00f6r B\u00fcy\u00fckl\u00fc\u011f\u00fc<\/a> hesaplay\u0131c\u0131lar\u0131na bak\u0131n.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130ki vekt\u00f6r\u00fcn X ve Y bile\u015fenlerini girerek aralar\u0131ndaki a\u00e7\u0131y\u0131 derece cinsinden bulun. Hesaplay\u0131c\u0131, nokta \u00e7arp\u0131m form\u00fcl\u00fcn\u00fc kullan\u0131r ve fizik, geometri ile bilgisayar grafiklerinde kullan\u0131\u015fl\u0131d\u0131r.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[42],"class_list":["post-32","post","type-post","status-publish","format-standard","hentry","category-matematik","tag-geometri"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/32","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=32"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":2258,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/32\/revisions\/2258"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}