{"id":244,"date":"2023-07-10T14:29:46","date_gmt":"2023-07-10T14:29:46","guid":{"rendered":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/"},"modified":"2023-07-10T14:29:46","modified_gmt":"2023-07-10T14:29:46","slug":"persamaan-parametrik-bidang","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/","title":{"rendered":"Persamaan parametrik bidang"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan apa itu persamaan parametrik suatu denah dan cara menghitungnya (rumus). Selain itu, Anda akan dapat melihat contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-ecuaciones-parametricas-de-un-plano\"><\/span> Apa persamaan parametrik suatu bidang? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Dalam geometri analitik, <strong>persamaan parametrik suatu bidang<\/strong> adalah persamaan yang memungkinkan bidang apa pun dinyatakan secara matematis. Untuk mencari persamaan parametrik suatu bidang, kita hanya memerlukan sebuah titik dan dua vektor bebas linier yang dimiliki bidang tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"formula-de-las-ecuaciones-parametricas-del-plano\"><\/span> Perumusan persamaan parametrik denah <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Perhatikan sebuah titik dan dua vektor arah pada sebuah bidang:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{c} P(P_x,P_y,P_z) \\\\[2ex] \\vv{\\text{u}}=(\\text{u}_x,\\text{u}_y,\\text{u}_z)\\\\[2ex] \\vv{\\text{v}}=(\\text{v}_x,\\text{v}_y,\\text{v}_z)\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"95\" width=\"116\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong>Rumus persamaan parametrik suatu bidang<\/strong> adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-3f74da212d3f5f1c3a3002d71a4bed96_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex]  y=P_y + \\lambda  \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left;\"> Emas<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2b5c45836864531b8e37025dabadd24a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lambda\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-461fe1a58a75801541487ddf10d32abd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\mu\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah dua skalar, yaitu dua bilangan real.<\/p>\n<\/div>\n<p> Penting agar kedua vektor arah persamaan bidang tersebut bebas linier, yaitu mempunyai arah yang berbeda (tidak paralel). Jika tidak, persamaan di atas tidak mewakili rencana. <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/equations-planes.webp\" alt=\"persamaan parametrik bidang\" class=\"wp-image-2443\" width=\"404\" height=\"142\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Di sisi lain, perlu diingat bahwa selain persamaan parametrik, ada cara lain untuk menyatakan bidang dalam ruang secara analitis (dalam R3), seperti <a href=\"https:\/\/mathority.org\/id\/persamaan-bidang-umum-atau-kartesius-implisit\/\">persamaan bidang umum<\/a> . Di tautan ini Anda akan menemukan rumusnya, cara menghitungnya dari persamaan parametrik denah, contoh, dan latihan yang diselesaikan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-las-ecuaciones-parametricas-de-un-plano\"><\/span> Contoh cara mencari persamaan parametrik suatu bidang <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> Setelah kita melihat persamaan parametrik bidang, mari kita lihat cara menghitungnya menggunakan contoh:<\/p>\n<ul>\n<li> Temukan persamaan parametrik bidang yang melalui titik tersebut\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3f0118e7d45cb9daa5eb13da519c4c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan berisi vektor<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-181eea061c4ba593347d9a9418e929f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(2,0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1902a5430dccdf4883ac68065ccaad61_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}=(4,2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"88\" style=\"vertical-align: -5px;\"><\/p>\n<\/li>\n<\/ul>\n<p> Untuk menentukan persamaan parametrik denah tersebut, cukup terapkan rumusnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46f87775f11f01a59c70aa3ee864aebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan sekarang kita substitusikan titik dan masing-masing vektor arah ke dalam persamaan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-501ec8b26b4d88ebe95abd3ca7e7fe44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=1 + \\lambda \\cdot 2 + \\mu \\cdot 4 \\\\[1.7ex] y=3+ \\lambda \\cdot 0 + \\mu \\cdot 2\\\\[1.7ex] z=2 + \\lambda\\cdot (-1)+ \\mu \\cdot 3\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0e8517084217ee5519c428b598f2d7f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=1 + 2\\lambda + 4\\mu } \\\\[1.7ex] \\bm{y=3 + 2\\mu}\\\\[1.7ex] \\bm{z=2 -\\lambda+ 3\\mu} \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-pasar-de-la-ecuacion-vectorial-de-un-plano-a-ecuaciones-parametricas\"><\/span> Bagaimana berpindah dari persamaan vektor bidang ke persamaan parametrik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Cara lain untuk menentukan persamaan parametrik suatu bidang adalah dari persamaan vektor suatu bidang. Di bawah ini Anda dapat melihat demonya.<\/p>\n<p> Biarkan persamaan vektor bidang apa pun menjadi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-78b41d21b63c22ec05d3f93576a897e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+\\lambda (\\text{u}_x,\\text{u}_y,\\text{u}_z) + \\mu (\\text{v}_x,\\text{v}_y,\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"398\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Kami mengoperasikan dan pertama-tama melakukan perkalian vektor dengan skalar:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eb7c00ddf8ba235e3698c85a0f23db0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x,P_y,P_z)+ (\\lambda\\text{u}_x,\\lambda\\text{u}_y,\\lambda\\text{u}_z) +(\\mu\\text{v}_x,\\mu\\text{v}_y,\\mu\\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"440\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Selanjutnya kita tambahkan komponen-komponennya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e3ff52d13a3d4400800b0f72148f99c4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_x+\\lambda \\text{u}_x + \\mu \\text{v}_x,P_y+\\lambda \\text{u}_y + \\mu \\text{v}_y,P_z+\\lambda \\text{u}_z + \\mu \\text{v}_z)\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"467\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Dan terakhir, kita memperoleh persamaan parametrik bidang dengan mengasimilasi koordinat yang bersesuaian dengan setiap variabel secara terpisah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-46f87775f11f01a59c70aa3ee864aebe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y\\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Seperti yang Anda lihat pada dua contoh di atas, mencari persamaan parametrik sebuah bidang relatif mudah. Namun, soalnya bisa menjadi sedikit rumit, jadi di bawah ini Anda memiliki beberapa latihan yang diselesaikan dengan tingkat kesulitan berbeda sehingga Anda bisa berlatih. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-ecuaciones-parametricas-del-plano\"><\/span> Memecahkan masalah persamaan parametrik bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan persamaan parametrik bidang yang memuat vektor<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-490c9a9e1ad20441fc3e4e552562da06_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}=(2,1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"89\" style=\"vertical-align: -5px;\"><\/p>\n<p> dan melewati dua poin berikut:<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e0c8787181ac89109302dca999a33418_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,2,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\"><\/p>\n<p> Dan <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b15174216dceaaf397f378acb645116_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(-2,-1,1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mengetahui persamaan suatu bidang, diperlukan sebuah titik dan dua vektor dan dalam hal ini kita hanya mempunyai satu vektor, oleh karena itu kita harus mencari vektor pengarah bidang lainnya. Untuk melakukan ini, kita dapat menghitung vektor yang mendefinisikan dua titik pada bidang:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42b4f718ed5e9e490fb0129949f8f694_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (-2,-1,1) - (3,2,-1) = (-5,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita telah mengetahui dua vektor arah bidang dan sebuah titik, maka kita menggunakan rumus persamaan parametrik bidang:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita substitusikan dua vektor dan salah satu dari dua titik pada bidang tersebut ke dalam persamaan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ecedfca92c24d2754bcca977f2f30e76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=3 + \\lambda \\cdot 2+ \\mu \\cdot (-5) \\\\[1.7ex] y=2 + \\lambda \\cdot 1 + \\mu \\cdot (-3) \\\\[1.7ex] z=(-1) + \\lambda\\cdot 5 + \\mu \\cdot 2 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"190\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c67219e6157433f05d410c0aefb05f05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=3 +2 \\lambda-5\\mu } \\\\[1.7ex] \\bm{y=2 + \\lambda-3 \\mu } \\\\[1.7ex] \\bm{z=-1 + 5\\lambda + 2\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"151\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 2<\/h3>\n<p> Temukan persamaan parametrik bidang yang memuat tiga titik berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-df564519d92ccbe87c5500460231d2b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(4,1,0) \\qquad B(2,-3,-1) \\qquad C(1,5,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"308\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mencari persamaan parametrik bidang tersebut, kita perlu mencari dua vektor bebas linier yang terhubung dalam bidang tersebut. Dan untuk ini, kita dapat menghitung dua vektor yang ditentukan oleh 3 titik: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-14d7f4f29cbdc14a69357bf1b8f29b4e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,-3,-1) - (4,1,0) = (-2,-4,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"406\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0a33c0974226c3e3c0a51de22c0b8b38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AC} = C - A = (1,5,3) - (4,1,0) = (-3,4,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"350\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Koordinat kedua vektor yang ditemukan tidak proporsional, sehingga saling bebas linier.<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita telah mengetahui dua vektor arah dan sebuah titik pada bidang, kita menerapkan rumus persamaan parametrik bidang:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kita substitusikan dua vektor dan salah satu dari tiga titik pada bidang tersebut ke dalam persamaan: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f57edaf8a85108cffb796470ffca8484_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=4 + \\lambda \\cdot (-2)+ \\mu \\cdot (-3) \\\\[1.7ex] y=1 + \\lambda \\cdot (-4) + \\mu \\cdot 4 \\\\[1.7ex] z=0 + \\lambda\\cdot (-1) + \\mu \\cdot 3 \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"218\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cab5ddc074bd7df6849d71854207cf5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=4 -2 \\lambda-3\\mu } \\\\[1.7ex] \\bm{y=1-4 \\lambda+4 \\mu } \\\\[1.7ex] \\bm{z=-\\lambda + 3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"138\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 3<\/h3>\n<p> Hitung persamaan parametrik bidang yang ditentukan oleh persamaan vektor berikut: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01df6ae373f0d460332985a54715ca88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,-1,5)+\\lambda (6,1,-2) + \\mu (1,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mengubah persamaan vektor bidang menjadi persamaan parametrik, Anda harus mengoperasikan koordinatnya lalu menyelesaikan setiap variabel secara terpisah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-01df6ae373f0d460332985a54715ca88_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,-1,5)+\\lambda (6,1,-2) + \\mu (1,-1,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0b2bc3ea152efd43fbb9a16f7d1c73b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(0,-1,5)+(6\\lambda,\\lambda,-2\\lambda) + (\\mu,-\\mu,3\\mu)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"370\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-8760242bbd8cf85b3d2e7280e1c0a2e5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(6\\lambda+\\mu,-1+\\lambda-\\mu,5-2\\lambda+3\\mu)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"339\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-381b1ceea87f332904ae69a566ecd1af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=6\\lambda+\\mu } \\\\[1.7ex] \\bm{y=-1+\\lambda-\\mu} \\\\[1.7ex] \\bm{z=5-2\\lambda+3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Temukan persamaan parametrik bidang yang memuat garis<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan sejajar dengan kanan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> menjadi garis: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-624f315685b292c4bb05e9cb4b931a97_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=1+t \\\\[1.7ex] y=2-3t\\\\[1.7ex] z=4+2t \\end{cases} \\qquad \\qquad s: \\ \\frac{x-4}{2} = \\frac{y+3}{2}= \\frac{z-2}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"424\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mencari persamaan parametrik bidang, kita perlu mengetahui dua vektor arah dan sebuah titik pada bidang tersebut. Instruksi memberitahu kita bahwa itu berisi garis<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> Oleh karena itu, kita dapat mengambil vektor arah dan sebuah titik pada garis ini untuk mendefinisikan bidang tersebut. Lebih lanjut pernyataan tersebut menyatakan bahwa bidang tersebut sejajar dengan garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4cc36ef269909ae645021a09d5e91016_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> jadi kita juga bisa menggunakan vektor arah garis ini untuk persamaan bidangnya.<\/p>\n<p class=\"has-text-align-left\"> hak<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dinyatakan dalam bentuk persamaan parametrik, sehingga komponen vektor arahnya adalah koefisien suku parameter<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6b40bdea86f773b36fb40078fb4ddf23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(1,-3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan koordinat Cartesian suatu titik pada garis yang sama adalah suku-suku bebas dari persamaan parametrik:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d565383a925076ae118032f7b9b62f7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(1,2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sebaliknya garis lurus<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> berbentuk persamaan kontinu sehingga komponen vektor arahnya adalah penyebut pecahan:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a8f571b217df7a6bbe833d706091457a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{s} =(2,2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, persamaan parametrik dari denah tersebut adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f5adabb85c9285653d6b638f7c48ba50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=P_x + \\lambda \\text{u}_x + \\mu \\text{v}_x \\\\[1.7ex] y=P_y + \\lambda \\text{u}_y + \\mu \\text{v}_y \\\\[1.7ex] z=P_z + \\lambda\\text{u}_z + \\mu \\text{v}_z \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"167\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c81f4d8e5aa907f111b3389d5137736e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}x=1 + \\lambda \\cdot 1+ \\mu \\cdot 2 \\\\[1.7ex] y=2 + \\lambda \\cdot (-3) + \\mu \\cdot 2 \\\\[1.7ex] z=4 + \\lambda\\cdot 2 + \\mu \\cdot (-3) \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"189\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fccd86ac9a3e4084e324d8e5b1071e59_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{cases}\\bm{x=1 + \\lambda+2\\mu } \\\\[1.7ex] \\bm{y=2-3 \\lambda+2 \\mu } \\\\[1.7ex] \\bm{z=4+2\\lambda -3\\mu } \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"107\" width=\"137\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan apa itu persamaan parametrik suatu denah dan cara menghitungnya (rumus). Selain itu, Anda akan dapat melihat contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. Apa persamaan parametrik suatu bidang? Dalam geometri analitik, persamaan parametrik suatu bidang adalah persamaan yang memungkinkan bidang apa pun dinyatakan secara matematis. Untuk &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\"> <span class=\"screen-reader-text\">Persamaan parametrik bidang<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[47],"tags":[],"class_list":["post-244","post","type-post","status-publish","format-standard","hentry","category-titik-garis-dan-bidang"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Persamaan parametrik bidang - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Persamaan parametrik bidang - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan apa itu persamaan parametrik suatu denah dan cara menghitungnya (rumus). Selain itu, Anda akan dapat melihat contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. Apa persamaan parametrik suatu bidang? Dalam geometri analitik, persamaan parametrik suatu bidang adalah persamaan yang memungkinkan bidang apa pun dinyatakan secara matematis. Untuk &hellip; Persamaan parametrik bidang Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T14:29:46+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Persamaan parametrik bidang\",\"datePublished\":\"2023-07-10T14:29:46+00:00\",\"dateModified\":\"2023-07-10T14:29:46+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\"},\"wordCount\":684,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Titik, garis, dan bidang\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\",\"url\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\",\"name\":\"Persamaan parametrik bidang - Mathority\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/#website\"},\"datePublished\":\"2023-07-10T14:29:46+00:00\",\"dateModified\":\"2023-07-10T14:29:46+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#breadcrumb\"},\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathority.org\/id\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Persamaan parametrik bidang\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathority.org\/id\/#website\",\"url\":\"https:\/\/mathority.org\/id\/\",\"name\":\"Mathority\",\"description\":\"Di mana rasa ingin tahu bertemu dengan perhitungan!\",\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathority.org\/id\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"id\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathority.org\/id\/#organization\",\"name\":\"Mathority\",\"url\":\"https:\/\/mathority.org\/id\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"contentUrl\":\"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png\",\"width\":703,\"height\":151,\"caption\":\"Mathority\"},\"image\":{\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/\"}},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\",\"name\":\"Tim Mathority\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"id\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g\",\"caption\":\"Tim Mathority\"},\"sameAs\":[\"http:\/\/mathority.org\/id\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Persamaan parametrik bidang - Mathority","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:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/","og_locale":"id_ID","og_type":"article","og_title":"Persamaan parametrik bidang - Mathority","og_description":"Di halaman ini Anda akan menemukan apa itu persamaan parametrik suatu denah dan cara menghitungnya (rumus). Selain itu, Anda akan dapat melihat contoh dan latihan dengan latihan yang diselesaikan langkah demi langkah. Apa persamaan parametrik suatu bidang? Dalam geometri analitik, persamaan parametrik suatu bidang adalah persamaan yang memungkinkan bidang apa pun dinyatakan secara matematis. Untuk &hellip; Persamaan parametrik bidang Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/","article_published_time":"2023-07-10T14:29:46+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cf5d4130501bb01b15aa80f8f80caf1a_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"3 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Persamaan parametrik bidang","datePublished":"2023-07-10T14:29:46+00:00","dateModified":"2023-07-10T14:29:46+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/"},"wordCount":684,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Titik, garis, dan bidang"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/","url":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/","name":"Persamaan parametrik bidang - Mathority","isPartOf":{"@id":"https:\/\/mathority.org\/id\/#website"},"datePublished":"2023-07-10T14:29:46+00:00","dateModified":"2023-07-10T14:29:46+00:00","breadcrumb":{"@id":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#breadcrumb"},"inLanguage":"id","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathority.org\/id\/persamaan-parametrik-bidang\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathority.org\/id\/"},{"@type":"ListItem","position":2,"name":"Persamaan parametrik bidang"}]},{"@type":"WebSite","@id":"https:\/\/mathority.org\/id\/#website","url":"https:\/\/mathority.org\/id\/","name":"Mathority","description":"Di mana rasa ingin tahu bertemu dengan perhitungan!","publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathority.org\/id\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"id"},{"@type":"Organization","@id":"https:\/\/mathority.org\/id\/#organization","name":"Mathority","url":"https:\/\/mathority.org\/id\/","logo":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/","url":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","contentUrl":"https:\/\/mathority.org\/id\/wp-content\/uploads\/2023\/09\/mathority-logo.png","width":703,"height":151,"caption":"Mathority"},"image":{"@id":"https:\/\/mathority.org\/id\/#\/schema\/logo\/image\/"}},{"@type":"Person","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38","name":"Tim Mathority","image":{"@type":"ImageObject","inLanguage":"id","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/8a35e4c8616d1c34c03ca02862b580f4372c5650665668489db53a09579bbc4f?s=96&d=mm&r=g","caption":"Tim Mathority"},"sameAs":["http:\/\/mathority.org\/id"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/244","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/comments?post=244"}],"version-history":[{"count":0,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/posts\/244\/revisions"}],"wp:attachment":[{"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/media?parent=244"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/categories?post=244"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathority.org\/id\/wp-json\/wp\/v2\/tags?post=244"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}