{"id":2034,"date":"2026-10-13T16:18:11","date_gmt":"2026-10-13T15:18:11","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/matematica\/produto-vetorial-3d\/"},"modified":"2026-10-13T16:18:11","modified_gmt":"2026-10-13T15:18:11","slug":"produto-vetorial-3d","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/matematica\/produto-vetorial-3d\/","title":{"rendered":"Calculadora de produto vetorial 3D"},"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\">Calcule o produto vetorial de dois vetores<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2034\" data-favorite-title=\"Produto vetorial 3D\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/matematica\/produto-vetorial-3d\/\" data-favorite-excerpt=\"Digite as componentes X, Y e Z de dois vetores para calcular o produto vetorial na hora. A calculadora mostra o vetor resultante, seu m\u00f3dulo e todo o c\u00e1lculo passo a passo.\" aria-label=\"Adicionar aos favoritos\" 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\/pt\/matematica\/produto-vetorial-3d\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2034\" data-post=\"2034\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Vetor A<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">A \u2014 componente X<\/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_componente_x\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"2\"\/><small id=\"calc-info-2\">Primeira componente do vetor A.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">A \u2014 componente Y<\/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_componente_y\" id=\"field-3\" aria-describedby=\"calc-info-3\" step=\"any\" value=\"3\"\/><small id=\"calc-info-3\">Segunda componente do vetor A.<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">A \u2014 componente Z<\/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_componente_z\" id=\"field-4\" aria-describedby=\"calc-info-4\" step=\"any\" value=\"4\"\/><small id=\"calc-info-4\">Terceira componente do vetor A.<\/small><\/div><div class=\"is-single field\" id=\"input-5\"><span class=\"font-semibold\">Vetor B<\/span><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">B \u2014 componente X<\/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_componente_x\" id=\"field-6\" aria-describedby=\"calc-info-6\" step=\"any\" value=\"5\"\/><small id=\"calc-info-6\">Primeira componente do vetor B.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">B \u2014 componente Y<\/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_componente_y\" id=\"field-7\" aria-describedby=\"calc-info-7\" step=\"any\" value=\"6\"\/><small id=\"calc-info-7\">Segunda componente do vetor B.<\/small><\/div><div class=\"field has-term\" id=\"input-8\"><label for=\"field-8\">B \u2014 componente Z<\/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_componente_z\" id=\"field-8\" aria-describedby=\"calc-info-8\" step=\"any\" value=\"7\"\/><small id=\"calc-info-8\">Terceira componente do vetor B.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2034\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/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> Seu produto vetorial<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Vetor do produto vetorial<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Componente X<\/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=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Componente Y<\/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=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Componente Z<\/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=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>M\u00f3dulo<\/span><span class=\"result-term\">|C|<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Etapas do c\u00e1lculo<\/span><\/span><span class=\"field-value\" id=\"result-6\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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\">Copiar link para este c\u00e1lculo<\/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>Deixar um coment\u00e1rio<\/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=\"2034\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/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\">Curti <\/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\">\u00datil <\/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\">Confuso <\/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\">Decepcionado <\/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\">Impreciso <\/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>F\u00f3rmula do produto vetorial 3D<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/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>Onde:<\/strong><\/p>\n<ul>\n<li>\\(A_x, A_y, A_z\\) \u2014 componentes do primeiro vetor \\(\\mathbf{A}\\)<\/li>\n<li>\\(B_x, B_y, B_z\\) \u2014 componentes do segundo vetor \\(\\mathbf{B}\\)<\/li>\n<li>\\(C_x, C_y, C_z\\) \u2014 componentes do produto vetorial \\(\\mathbf{C}\\)<\/li>\n<li>\\(|\\mathbf{C}|\\) \u2014 m\u00f3dulo (comprimento) do produto vetorial<\/li>\n<\/ul>\n<p>O produto vetorial \\(\\mathbf{A} \\times \\mathbf{B}\\) gera um novo vetor perpendicular a \\(\\mathbf{A}\\) e a \\(\\mathbf{B}\\), cujo m\u00f3dulo \u00e9 igual \u00e0 \u00e1rea do paralelogramo formado por eles.<\/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>Produto vetorial 3D \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> calcule o produto vetorial de \\(\\mathbf{A} = (2, 3, 4)\\) e \\(\\mathbf{B} = (5, 6, 7)\\).<\/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>Resultado:<\/strong> \\(\\mathbf{A} \\times \\mathbf{B} = (-3,\\ 6,\\ -3)\\), com m\u00f3dulo \\(\\approx 7.348\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora de produto vetorial 3D<\/h2>\n<ol>\n<li>Digite as tr\u00eas componentes do primeiro vetor nos campos <strong>A \u2014 componente X<\/strong>, <strong>A \u2014 componente Y<\/strong> e <strong>A \u2014 componente Z<\/strong>.<\/li>\n<li>Digite as tr\u00eas componentes do segundo vetor nos campos <strong>B \u2014 componente X<\/strong>, <strong>B \u2014 componente Y<\/strong> e <strong>B \u2014 componente Z<\/strong>.<\/li>\n<li>Valores negativos e zero s\u00e3o aceitos \u2014 basta digitar o sinal de menos onde for necess\u00e1rio.<\/li>\n<li>Leia o resultado em <strong>Seu produto vetorial<\/strong>: as componentes X, Y e Z do vetor resultante, o m\u00f3dulo dele e a resolu\u00e7\u00e3o passo a passo de cada c\u00e1lculo.<\/li>\n<\/ol>\n<h2>O que \u00e9 o produto vetorial?<\/h2>\n<p>O produto vetorial (tamb\u00e9m chamado de produto cruzado) \u00e9 uma opera\u00e7\u00e3o entre dois vetores no espa\u00e7o tridimensional. Diferente do produto escalar, que devolve um \u00fanico n\u00famero, o produto vetorial devolve um <em>vetor<\/em>. Sua dire\u00e7\u00e3o \u00e9 perpendicular ao plano que cont\u00e9m os dois vetores de entrada e \u00e9 determinada pela regra da m\u00e3o direita: aponte os dedos da m\u00e3o direita na dire\u00e7\u00e3o de \\(\\mathbf{A}\\), curve-os na dire\u00e7\u00e3o de \\(\\mathbf{B}\\) e seu polegar apontar\u00e1 na dire\u00e7\u00e3o de \\(\\mathbf{A} \\times \\mathbf{B}\\).<\/p>\n<p>A ordem dos vetores importa. Troc\u00e1-los inverte o sinal de todas as componentes: \\(\\mathbf{B} \\times \\mathbf{A} = -(\\mathbf{A} \\times \\mathbf{B})\\). Essa propriedade, chamada anticomutatividade, significa que o produto vetorial <em>n\u00e3o<\/em> \u00e9 comutativo \u2014 digitar os vetores em outra ordem d\u00e1 outra resposta.<\/p>\n<p>O m\u00f3dulo do produto vetorial tem um significado geom\u00e9trico:<\/p>\n<p>\\[ |\\mathbf{A} \\times \\mathbf{B}| = |\\mathbf{A}|\\,|\\mathbf{B}| \\sin\\theta \\]<\/p>\n<p>onde \\(\\theta\\) \u00e9 o \u00e2ngulo entre os dois vetores. Esse valor \u00e9 igual \u00e0 \u00e1rea do paralelogramo formado por \\(\\mathbf{A}\\) e \\(\\mathbf{B}\\). Se o resultado for o vetor nulo, os dois vetores s\u00e3o paralelos (ou um deles \u00e9 nulo), pois \\(\\sin 0\u00b0 = 0\\). Quanto maior o \u00e2ngulo entre os vetores, maior o m\u00f3dulo do produto vetorial \u2014 ele atinge o m\u00e1ximo quando os vetores s\u00e3o perpendiculares.<\/p>\n<p>O produto vetorial aparece em toda a f\u00edsica e a engenharia: o torque \u00e9 \\(\\mathbf{r} \\times \\mathbf{F}\\), a for\u00e7a magn\u00e9tica envolve \\(\\mathbf{v} \\times \\mathbf{B}\\) e o momento angular \u00e9 \\(\\mathbf{r} \\times \\mathbf{p}\\). Em computa\u00e7\u00e3o gr\u00e1fica, o produto vetorial \u00e9 usado para calcular as normais de superf\u00edcie na ilumina\u00e7\u00e3o e no sombreamento.<\/p>\n<h2>Premissas, limita\u00e7\u00f5es e dicas pr\u00e1ticas<\/h2>\n<ul>\n<li><strong>Somente tr\u00eas dimens\u00f5es.<\/strong> O produto vetorial s\u00f3 est\u00e1 definido para vetores 3D (existe uma vers\u00e3o limitada para vetores 2D, que devolve um escalar). Esta calculadora exige as tr\u00eas componentes de cada vetor.<\/li>\n<li><strong>A ordem importa.<\/strong> Se o seu resultado tiver sinal oposto ao do livro, verifique se a obra calculou \\(\\mathbf{B} \\times \\mathbf{A}\\) em vez de \\(\\mathbf{A} \\times \\mathbf{B}\\).<\/li>\n<li><strong>Verifica\u00e7\u00e3o de perpendicularidade.<\/strong> Uma forma r\u00e1pida de conferir o resultado: os produtos escalares \\(\\mathbf{A} \\cdot \\mathbf{C}\\) e \\(\\mathbf{B} \\cdot \\mathbf{C}\\) devem ser iguais a zero, j\u00e1 que o produto vetorial \u00e9 perpendicular aos dois vetores de entrada.<\/li>\n<li><strong>Vetores paralelos.<\/strong> Se o resultado for o vetor nulo \\((0, 0, 0)\\), os vetores de entrada s\u00e3o paralelos ou um deles \u00e9 nulo \u2014 \u00e9 um resultado v\u00e1lido, n\u00e3o um erro.<\/li>\n<li><strong>Unidades.<\/strong> As componentes devem usar unidades consistentes. Se \\(\\mathbf{A}\\) est\u00e1 em metros e \\(\\mathbf{B}\\) em newtons, o produto vetorial fica em newtons-metro (N\u00b7m), a unidade de torque.<\/li>\n<\/ul>\n<p>Se voc\u00ea precisar revisar a aritm\u00e9tica b\u00e1sica por tr\u00e1s das multiplica\u00e7\u00f5es entre componentes, a <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-de-multiplicacao\/\">calculadora de multiplica\u00e7\u00e3o<\/a> e a <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-de-subtracao\/\">calculadora de subtra\u00e7\u00e3o<\/a> podem cuidar de cada etapa individual.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Digite as componentes X, Y e Z de dois vetores para calcular o produto vetorial na hora. A calculadora mostra o vetor resultante, seu m\u00f3dulo e todo o c\u00e1lculo passo a passo.<\/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-2034","post","type-post","status-publish","format-standard","hentry","category-matematica","tag-geometria"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2034","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=2034"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2034\/revisions"}],"predecessor-version":[{"id":2404,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2034\/revisions\/2404"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2034"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2034"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2034"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}