{"id":3908,"date":"2026-10-14T06:41:53","date_gmt":"2026-10-14T05:41:53","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/matematik\/3b-vektorel-carpim-hesaplama\/"},"modified":"2026-10-14T06:41:53","modified_gmt":"2026-10-14T05:41:53","slug":"3b-vektorel-carpim-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/matematik\/3b-vektorel-carpim-hesaplama\/","title":{"rendered":"3B Vekt\u00f6rel \u00c7arp\u0131m Hesaplama Arac\u0131"},"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 Vekt\u00f6r\u00fcn Vekt\u00f6rel \u00c7arp\u0131m\u0131n\u0131 Bulun<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"3908\" data-favorite-title=\"3B Vekt\u00f6rel \u00c7arp\u0131m\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/matematik\/3b-vektorel-carpim-hesaplama\/\" data-favorite-excerpt=\"\u0130ki vekt\u00f6r\u00fcn X, Y ve Z bile\u015fenlerini girin ve vekt\u00f6rel \u00e7arp\u0131mlar\u0131n\u0131 an\u0131nda bulun. Hesaplama arac\u0131; sonu\u00e7 vekt\u00f6r\u00fcn\u00fc, b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc ve t\u00fcm ad\u0131m ad\u0131m hesaplamay\u0131 g\u00f6sterir.\" 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\/3b-vektorel-carpim-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-3908\" data-post=\"3908\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">A vekt\u00f6r\u00fc<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">A \u2014 X bile\u015feni<\/label><div class=\"term\">A\u2093<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a_x_bileeni\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"2\"\/><small id=\"calc-info-2\">A vekt\u00f6r\u00fcn\u00fcn birinci bile\u015feni.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">A \u2014 Y bile\u015feni<\/label><div class=\"term\">A\u1d67<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a_y_bileeni\" id=\"field-3\" aria-describedby=\"calc-info-3\" step=\"any\" value=\"3\"\/><small id=\"calc-info-3\">A vekt\u00f6r\u00fcn\u00fcn ikinci bile\u015feni.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">A \u2014 Z bile\u015feni<\/label><div class=\"term\">A_z<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"a_z_bileeni\" id=\"field-4\" aria-describedby=\"calc-info-4\" step=\"any\" value=\"4\"\/><small id=\"calc-info-4\">A vekt\u00f6r\u00fcn\u00fcn \u00fc\u00e7\u00fcnc\u00fc bile\u015feni.<\/small><\/div><div class=\"is-single field\" id=\"input-5\"><span class=\"font-semibold\">B vekt\u00f6r\u00fc<\/span><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">B \u2014 X bile\u015feni<\/label><div class=\"term\">B\u2093<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"b_x_bileeni\" id=\"field-6\" aria-describedby=\"calc-info-6\" step=\"any\" value=\"5\"\/><small id=\"calc-info-6\">B vekt\u00f6r\u00fcn\u00fcn birinci bile\u015feni.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">B \u2014 Y bile\u015feni<\/label><div class=\"term\">B\u1d67<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"b_y_bileeni\" id=\"field-7\" aria-describedby=\"calc-info-7\" step=\"any\" value=\"6\"\/><small id=\"calc-info-7\">B vekt\u00f6r\u00fcn\u00fcn ikinci bile\u015feni.<\/small><\/div><div class=\"field has-term\" id=\"input-8\"><label for=\"field-8\">B \u2014 Z bile\u015feni<\/label><div class=\"term\">B_z<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"b_z_bileeni\" id=\"field-8\" aria-describedby=\"calc-info-8\" step=\"any\" value=\"7\"\/><small id=\"calc-info-8\">B vekt\u00f6r\u00fcn\u00fcn \u00fc\u00e7\u00fcnc\u00fc bile\u015feni.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"3908\">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> Vekt\u00f6rel \u00c7arp\u0131m\u0131n\u0131z<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>\u00c7arp\u0131m Vekt\u00f6r\u00fc<\/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 class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>X Bile\u015feni<\/span><span class=\"result-term\">C\u2093<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/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 class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Y Bile\u015feni<\/span><span class=\"result-term\">C\u1d67<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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 class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>Z Bile\u015feni<\/span><span class=\"result-term\">C_z<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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 class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>B\u00fcy\u00fckl\u00fck<\/span><span class=\"result-term\">|C|<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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 class=\"field-result is-column\" id=\"output-6\"><span class=\"field-title\"><span>Hesaplama Ad\u0131mlar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/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=\"3908\" 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>3B Vekt\u00f6rel \u00c7arp\u0131m 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\\[ \\mathbf{C} = \\mathbf{A} \\times \\mathbf{B} = \\begin{vmatrix} \\mathbf{i} &amp; \\mathbf{j} &amp; \\mathbf{k} \\\\ A_x &amp; A_y &amp; A_z \\\\ B_x &amp; B_y &amp; B_z \\end{vmatrix} \\]\n\\[ C_x = A_y B_z - A_z B_y, \\quad C_y = A_z B_x - A_x B_z, \\quad C_z = A_x B_y - A_y B_x \\]\n\\[ |\\mathbf{C}| = \\sqrt{C_x^2 + C_y^2 + C_z^2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Buradaki g\u00f6sterimler:<\/strong><\/p>\n<ul>\n<li>\\(A_x, A_y, A_z\\) \u2014 birinci vekt\u00f6r \\(\\mathbf{A}\\)'n\u0131n bile\u015fenleri<\/li>\n<li>\\(B_x, B_y, B_z\\) \u2014 ikinci vekt\u00f6r \\(\\mathbf{B}\\)'nin bile\u015fenleri<\/li>\n<li>\\(C_x, C_y, C_z\\) \u2014 vekt\u00f6rel \u00e7arp\u0131m \\(\\mathbf{C}\\)'nin bile\u015fenleri<\/li>\n<li>\\(|\\mathbf{C}|\\) \u2014 vekt\u00f6rel \u00e7arp\u0131m vekt\u00f6r\u00fcn\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc (uzunlu\u011fu)<\/li>\n<\/ul>\n<p>Vekt\u00f6rel \u00e7arp\u0131m \\(\\mathbf{A} \\times \\mathbf{B}\\), hem \\(\\mathbf{A}\\) hem de \\(\\mathbf{B}\\)'ye dik olan yeni bir vekt\u00f6r \u00fcretir; bu vekt\u00f6r\u00fcn b\u00fcy\u00fckl\u00fc\u011f\u00fc, iki vekt\u00f6r\u00fcn olu\u015fturdu\u011fu paralelkenar\u0131n alan\u0131na e\u015fittir.<\/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>3B Vekt\u00f6rel \u00c7arp\u0131m \u2013 \u00d6rnek Hesaplama<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> \\(\\mathbf{A} = (2, 3, 4)\\) ve \\(\\mathbf{B} = (5, 6, 7)\\) vekt\u00f6rlerinin vekt\u00f6rel \u00e7arp\u0131m\u0131n\u0131 bulal\u0131m.<\/p>\n<p>\\[ C_x = A_y B_z - A_z B_y = 3 \\cdot 7 - 4 \\cdot 6 = 21 - 24 = -3 \\]<\/p>\n<p>\\[ C_y = A_z B_x - A_x B_z = 4 \\cdot 5 - 2 \\cdot 7 = 20 - 14 = 6 \\]<\/p>\n<p>\\[ C_z = A_x B_y - A_y B_x = 2 \\cdot 6 - 3 \\cdot 5 = 12 - 15 = -3 \\]<\/p>\n<p>\\[ |\\mathbf{C}| = \\sqrt{(-3)^2 + 6^2 + (-3)^2} = \\sqrt{54} \\approx 7.348 \\]<\/p>\n<p><strong>Sonu\u00e7:<\/strong> \\(\\mathbf{A} \\times \\mathbf{B} = (-3,\\ 6,\\ -3)\\), b\u00fcy\u00fckl\u00fc\u011f\u00fc \\(\\approx 7.348\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>3B Vekt\u00f6rel \u00c7arp\u0131m Hesaplama Arac\u0131 Nas\u0131l Kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>Birinci vekt\u00f6r\u00fcn \u00fc\u00e7 bile\u015fenini <strong>A \u2014 X bile\u015feni<\/strong>, <strong>A \u2014 Y bile\u015feni<\/strong> ve <strong>A \u2014 Z bile\u015feni<\/strong> alanlar\u0131na girin.<\/li>\n<li>\u0130kinci vekt\u00f6r\u00fcn \u00fc\u00e7 bile\u015fenini <strong>B \u2014 X bile\u015feni<\/strong>, <strong>B \u2014 Y bile\u015feni<\/strong> ve <strong>B \u2014 Z bile\u015feni<\/strong> alanlar\u0131na girin.<\/li>\n<li>Negatif de\u011ferler ve s\u0131f\u0131r kabul edilir \u2014 gerekli yerlere eksi i\u015faretini yazman\u0131z yeterlidir.<\/li>\n<li><strong>Vekt\u00f6rel \u00c7arp\u0131m\u0131n\u0131z<\/strong> ba\u015fl\u0131\u011f\u0131 alt\u0131ndaki sonucu okuyun: sonu\u00e7 vekt\u00f6r\u00fcn\u00fcn X, Y ve Z bile\u015fenleri, b\u00fcy\u00fckl\u00fc\u011f\u00fc ve her hesaplaman\u0131n ad\u0131m ad\u0131m d\u00f6k\u00fcm\u00fc.<\/li>\n<\/ol>\n<h2>Vekt\u00f6rel \u00e7arp\u0131m nedir?<\/h2>\n<p>Vekt\u00f6rel \u00e7arp\u0131m (vekt\u00f6r \u00e7arp\u0131m\u0131 olarak da bilinir), \u00fc\u00e7 boyutlu uzayda iki vekt\u00f6re uygulanan bir i\u015flemdir. Tek bir say\u0131 veren skaler \u00e7arp\u0131m\u0131n aksine, vekt\u00f6rel \u00e7arp\u0131m bir <em>vekt\u00f6r<\/em> verir. Bu vekt\u00f6r\u00fcn y\u00f6n\u00fc, her iki giri\u015f vekt\u00f6r\u00fcn\u00fc i\u00e7eren d\u00fczleme diktir ve sa\u011f el kural\u0131yla belirlenir: sa\u011f elinizin parmaklar\u0131n\u0131 \\(\\mathbf{A}\\) y\u00f6n\u00fcnde uzat\u0131n, \\(\\mathbf{B}\\)'ye do\u011fru k\u0131v\u0131r\u0131n; ba\u015fparma\u011f\u0131n\u0131z \\(\\mathbf{A} \\times \\mathbf{B}\\) y\u00f6n\u00fcn\u00fc g\u00f6sterir.<\/p>\n<p>Vekt\u00f6rlerin s\u0131ras\u0131 \u00f6nemlidir. Yerlerini de\u011fi\u015ftirmek, t\u00fcm bile\u015fenlerin i\u015faretini tersine \u00e7evirir: \\(\\mathbf{B} \\times \\mathbf{A} = -(\\mathbf{A} \\times \\mathbf{B})\\). Antikom\u00fctatiflik ad\u0131 verilen bu \u00f6zellik, vekt\u00f6rel \u00e7arp\u0131m\u0131n <em>kom\u00fctatif olmad\u0131\u011f\u0131<\/em> anlam\u0131na gelir \u2014 vekt\u00f6rleri farkl\u0131 bir s\u0131rayla girerseniz farkl\u0131 bir sonu\u00e7 al\u0131rs\u0131n\u0131z.<\/p>\n<p>Vekt\u00f6rel \u00e7arp\u0131m\u0131n b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fcn geometrik bir anlam\u0131 vard\u0131r:<\/p>\n<p>\\[ |\\mathbf{A} \\times \\mathbf{B}| = |\\mathbf{A}|\\,|\\mathbf{B}| \\sin\\theta \\]<\/p>\n<p>burada \\(\\theta\\), iki vekt\u00f6r aras\u0131ndaki a\u00e7\u0131d\u0131r. Bu de\u011fer, \\(\\mathbf{A}\\) ve \\(\\mathbf{B}\\)'nin olu\u015fturdu\u011fu paralelkenar\u0131n alan\u0131na e\u015fittir. Sonu\u00e7 s\u0131f\u0131r vekt\u00f6r\u00fcyse, \\(\\sin 0\u00b0 = 0\\) oldu\u011fundan iki vekt\u00f6r paraleldir (ya da biri s\u0131f\u0131rd\u0131r). Vekt\u00f6rler aras\u0131ndaki a\u00e7\u0131 b\u00fcy\u00fcd\u00fck\u00e7e vekt\u00f6rel \u00e7arp\u0131m da b\u00fcy\u00fcr; vekt\u00f6rler dikken en b\u00fcy\u00fck de\u011ferine ula\u015f\u0131r.<\/p>\n<p>Vekt\u00f6rel \u00e7arp\u0131m, fizikte ve m\u00fchendislikte her yerde kar\u015f\u0131n\u0131za \u00e7\u0131kar: tork \\(\\mathbf{r} \\times \\mathbf{F}\\), manyetik kuvvet \\(\\mathbf{v} \\times \\mathbf{B}\\) i\u00e7erir, a\u00e7\u0131sal momentum ise \\(\\mathbf{r} \\times \\mathbf{p}\\)'dir. Bilgisayar grafiklerinde ise vekt\u00f6rel \u00e7arp\u0131m, ayd\u0131nlatma ve g\u00f6lgelendirme i\u00e7in y\u00fczey normallerinin hesaplanmas\u0131nda kullan\u0131l\u0131r.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Yaln\u0131zca \u00fc\u00e7 boyut.<\/strong> Vekt\u00f6rel \u00e7arp\u0131m yaln\u0131zca 3B vekt\u00f6rler i\u00e7in tan\u0131ml\u0131d\u0131r (2B vekt\u00f6rler i\u00e7in skaler veren s\u0131n\u0131rl\u0131 bir s\u00fcr\u00fcm\u00fc vard\u0131r). Bu hesaplama arac\u0131, her vekt\u00f6r\u00fcn \u00fc\u00e7 bile\u015feninin de girilmesini ister.<\/li>\n<li><strong>S\u0131ra \u00f6nemlidir.<\/strong> Ders kitab\u0131ndaki cevab\u0131n i\u015faretinin tersini al\u0131yorsan\u0131z, kitab\u0131n \\(\\mathbf{A} \\times \\mathbf{B}\\) yerine \\(\\mathbf{B} \\times \\mathbf{A}\\) hesaplay\u0131p hesaplamad\u0131\u011f\u0131n\u0131 kontrol edin.<\/li>\n<li><strong>Diklik denetimi.<\/strong> Sonucu do\u011frulaman\u0131n h\u0131zl\u0131 bir yolu: vekt\u00f6rel \u00e7arp\u0131m her iki giri\u015fe dik oldu\u011fundan, \\(\\mathbf{A} \\cdot \\mathbf{C}\\) ve \\(\\mathbf{B} \\cdot \\mathbf{C}\\) skaler \u00e7arp\u0131mlar\u0131n\u0131n ikisi de s\u0131f\u0131ra e\u015fit olmal\u0131d\u0131r.<\/li>\n<li><strong>Paralel vekt\u00f6rler.<\/strong> \u00c7\u0131kt\u0131 \\((0, 0, 0)\\) s\u0131f\u0131r vekt\u00f6r\u00fcyse, giri\u015fler paraleldir ya da biri s\u0131f\u0131rd\u0131r \u2014 bu ge\u00e7erli bir sonu\u00e7tur, hata de\u011fildir.<\/li>\n<li><strong>Birimler.<\/strong> Bile\u015fenler tutarl\u0131 birimlerde olmal\u0131d\u0131r. \\(\\mathbf{A}\\) metre, \\(\\mathbf{B}\\) ise newton cinsindense, vekt\u00f6rel \u00e7arp\u0131m newton-metre (N\u00b7m) cinsinden olur; bu, torkun birimidir.<\/li>\n<\/ul>\n<p>Bile\u015fen \u00e7arp\u0131mlar\u0131n\u0131n arkas\u0131ndaki temel aritmeti\u011fi tazelemeniz gerekiyorsa, <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/carpma-hesaplayici\/\">\u00e7arpma hesaplama arac\u0131<\/a> ve <a href=\"https:\/\/wpcalc.com\/tr\/matematik\/cikarma-hesaplayici\/\">\u00e7\u0131karma hesaplama arac\u0131<\/a> tek tek ad\u0131mlar\u0131 sizin yerine yapabilir.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0130ki vekt\u00f6r\u00fcn X, Y ve Z bile\u015fenlerini girin ve vekt\u00f6rel \u00e7arp\u0131mlar\u0131n\u0131 an\u0131nda bulun. Hesaplama arac\u0131; sonu\u00e7 vekt\u00f6r\u00fcn\u00fc, b\u00fcy\u00fckl\u00fc\u011f\u00fcn\u00fc ve t\u00fcm ad\u0131m ad\u0131m hesaplamay\u0131 g\u00f6sterir.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[42],"class_list":["post-3908","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\/3908","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=3908"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/3908\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=3908"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=3908"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=3908"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}