{"id":249,"date":"2023-07-10T12:11:22","date_gmt":"2023-07-10T12:11:22","guid":{"rendered":"https:\/\/mathority.org\/id\/posisi-relatif-dua-bidang-dalam-ruang-r3-contoh-latihan-yang-diselesaikan\/"},"modified":"2023-07-10T12:11:22","modified_gmt":"2023-07-10T12:11:22","slug":"posisi-relatif-dua-bidang-dalam-ruang-r3-contoh-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/posisi-relatif-dua-bidang-dalam-ruang-r3-contoh-latihan-yang-diselesaikan\/","title":{"rendered":"Posisi relatif dua bidang dalam ruang"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan semua kemungkinan posisi relatif dua bidang (bidang kering, sejajar, atau berhimpitan). Anda juga akan menemukan bagaimana posisi relatif antara dua bidang dihitung dan, sebagai tambahan, Anda akan dapat melihat contoh dan berlatih dengan latihan yang diselesaikan. <\/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%bfcuales-son-las-posiciones-relativas-de-dos-planos\"><\/span> Berapakah posisi relatif dua 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, hanya ada tiga kemungkinan posisi relatif antara dua bidang: bidang potong, bidang sejajar, dan bidang berimpit.<\/p>\n<ul>\n<li> <strong>Bidang berpotongan<\/strong> : Dua bidang berpotongan jika hanya berpotongan pada satu garis.<\/li>\n<li> <strong>Bidang sejajar<\/strong> : Dua bidang sejajar jika tidak berpotongan di titik mana pun.<\/li>\n<li> <strong>Bidang-bidang yang bersinggungan<\/strong> : Dua bidang dikatakan berhimpitan jika kedua bidang tersebut mempunyai titik-titik yang sama. <\/li>\n<\/ul>\n<div class=\"wp-block-columns is-layout-flex wp-container-72\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>pesawat yang berpotongan<\/strong> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-secants.webp\" alt=\"posisi relatif dua bidang yang berpotongan\" class=\"wp-image-2814\" width=\"265\" height=\"258\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>bidang paralel<\/strong> <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/plans-paralleles-1.webp\" alt=\"posisi relatif dua bidang sejajar\" class=\"wp-image-2815\" width=\"266\" height=\"166\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>pesawat yang kebetulan<\/strong> <\/p>\n<figure class=\"wp-block-image size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/deux-avions-coincidents.webp\" alt=\"kedudukan relatif dua bidang yang berhimpitan\" class=\"wp-image-2820\" width=\"294\" height=\"83\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Ada dua metode untuk mencari posisi relatif antara dua bidang: satu dari koefisien persamaan umum dua bidang dan yang lainnya dengan menghitung pangkat dua matriks. Berikut penjelasan masing-masing prosedurnya. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-determinar-la-posicion-relativa-de-dos-planos-por-coeficientes\"><\/span> Cara menentukan posisi relatif dua bidang berdasarkan koefisien<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Salah satu cara untuk mengetahui posisi relatif antara dua bidang adalah dengan menggunakan koefisien persamaan umum (atau implisit).<\/p>\n<p> Pertimbangkan persamaan umum (atau implisit) dari dua bidang berbeda:<\/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-a363201f1d61e53c35c3484a0fe116d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"221\" style=\"vertical-align: -4px;\"><\/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-330dffa3582cfbd92e893f755d2b06a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A'x+B'y+C'z+D'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"240\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Posisi relatif antara dua bidang dalam ruang tiga dimensi (dalam R3) bergantung pada proporsionalitas koefisien atau parameternya: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/position-relative-de-deux-plans-avec-parametres.webp\" alt=\"posisi relatif dua bidang dengan parameter\" class=\"wp-image-2825\" width=\"483\" height=\"263\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Oleh karena itu, kedua bidang akan berpotongan jika salah satu koefisien A, B, atau C tidak sebanding dengan koefisien lainnya. Sebaliknya, kedua bidang akan sejajar jika hanya suku-suku independennya saja yang tidak proporsional. Dan terakhir, rencana tersebut akan bertepatan jika semua koefisien dari kedua persamaan tersebut sebanding.<\/p>\n<p> Misalnya, mari kita hitung posisi relatif dua bidang 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-06ccd4d459bd8e4a4bfaa7722389c8ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 6x-2y+4z+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"200\" style=\"vertical-align: -4px;\"><\/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-0dc2e5222b977e7e3a1a3070b26ef4a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ -3x+y-2z+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"205\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Untuk mengetahui jenis pesawatnya, Anda perlu memeriksa koefisien mana yang sebanding:<\/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-fdce7ece2e3d326c1768ec8435fbb12c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{-3} = \\cfrac{-2}{1} =\\cfrac{4}{-2} \\neq \\cfrac{5}{4}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"162\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Koefisien A, B, dan C sebanding satu sama lain tetapi tidak sebanding dengan koefisien D, sehingga <strong>kedua bidang tersebut sejajar<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-posicion-relativa-de-dos-planos-por-rangos\"><\/span> Cara menghitung posisi relatif dua bidang berdasarkan jarak <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> Cara lain untuk mengetahui posisi relatif dua bidang tertentu adalah dengan menghitung jangkauan dua matriks yang dibentuk oleh koefisien bidang tersebut.<\/p>\n<p> Jadi, mari kita buat persamaan umum (atau implisit) dari dua bidang berbeda:<\/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-a363201f1d61e53c35c3484a0fe116d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ Ax+By+Cz+D=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"221\" style=\"vertical-align: -4px;\"><\/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-330dffa3582cfbd92e893f755d2b06a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ A'x+B'y+C'z+D'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"240\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Kita menyebut A sebagai matriks yang terdiri dari koefisien A, B, dan C dari dua 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-37f97413606a79781a34e0664a780b35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix} A&amp;B&amp;C\\\\[1.1ex] A&amp;B&amp;C\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"135\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan misalkan matriks A&#8217; adalah matriks yang diperluas dengan semua koefisien kedua 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-534e5baa11d1331cda0fa48c167a322f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A' =\\begin{pmatrix} A&amp;B&amp;C&amp;D\\\\[1.1ex] A&amp;B&amp;C&amp;D'\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"175\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Posisi relatif kedua bidang dapat diketahui berdasarkan rentang kedua matriks sebelumnya:<\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><\/figure>\n<p> Bahwa posisi relatif bergantung pada pangkat kedua matriks ini dapat ditunjukkan dari toerem Rouche-Frobenius (teorema yang digunakan untuk menyelesaikan sistem persamaan linier). Namun pada halaman ini kami tidak akan melakukan demonstrasi karena tidak perlu diketahui dan juga tidak memberikan banyak manfaat.<\/p>\n<p> Agar Anda dapat melihat cara melakukannya, kami akan menghitung posisi relatif antara dua bidang 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-bb7ab1c6ff6922119d6c9bdf8d00185d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 2x+3y-z+1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\"><\/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-615620cd79e191209135368785788ed5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x-4y+2=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"161\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Hal pertama yang harus dilakukan adalah membuat matriks A dan matriks perluasan A&#8217; dengan koefisien persamaan kedua 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-c5cfb4d05d76542970c1f7db9ef1b31a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A =\\begin{pmatrix} 2&amp;3&amp;-1\\\\[1.1ex] 3&amp;-4&amp;0\\end{pmatrix} \\qquad \\qquad A' =\\begin{pmatrix} 2&amp;3&amp;-1&amp;1\\\\[1.1ex] 3&amp;-4&amp;0&amp;2\\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"402\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan sekarang kita perlu menghitung rank masing-masing matriks. Pertama-tama kita mencari luas matriks A dengan determinannya: <\/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-5db59e1c8bbf94b95483870d47cea1b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A) = \\ ?\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" 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-2ad5c0df1a15c695be7c0c5c71304cc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{vmatrix} 2&amp;3\\\\[1.1ex] 3&amp;-4\\end{vmatrix} =-17\\neq 0\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"145\" 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-ef18656c1a261aa20598fc8f6a587323_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A) = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"76\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Matriks A memuat submatriks berukuran 2\u00d72 yang determinannya berbeda dengan nol, sehingga merupakan matriks berpangkat 2.<\/p>\n<p> Di sisi lain, perlu juga menghitung rank matriks A&#8217;. Dan pangkat matriks A&#8217; yang diperluas setidak-tidaknya akan selalu sama dengan pangkat matriks A, oleh karena itu, dalam kasus khusus ini pangkat matriks A&#8217; juga sama dengan 2.<\/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-c233de165178bb10a2af16fcdcba7412_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"rg(A') = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"81\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sehingga luasan kedua matriks tersebut ekuivalen dan bernilai 2, maka <strong>kedua bidang tersebut berpotongan<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-posicion-relativa-de-dos-planos\"><\/span>Memecahkan masalah posisi relatif dua bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Pelajari posisi relatif dua bidang 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-98683696adfea865d08a178dd9ba0254_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+3y-2z-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"191\" style=\"vertical-align: -4px;\"><\/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-2f74673e269babed8b8307b75abe8864_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 3x+9y-6z-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/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 menghitung posisi relatif antara dua bidang, kita akan melihat apakah koefisien persamaan kedua bidang sebanding:<\/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-c3fdba96e5ae97a2461c53ba81ce0f6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{3}= \\cfrac{3}{9} =\\cfrac{-2}{-6} = \\cfrac{-1}{-3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"156\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Semua koefisien persamaan implisit kedua bidang tersebut sebanding satu sama lain, <strong>oleh karena itu keduanya merupakan dua bidang yang berhimpitan<\/strong> .<\/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> Tentukan posisi relatif dua bidang 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-bb9ae2ea33c20a52892a0a0a1916d1a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x+3y-z+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"182\" style=\"vertical-align: -4px;\"><\/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-ed4d3289afe5e58aa256afcb9937ae0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 2x+3y-2z+8=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"200\" style=\"vertical-align: -4px;\"><\/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 menentukan posisi relatif antara dua bidang, kita akan menganalisis proporsionalitas koefisien persamaannya:<\/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-9c1a39300d950ead0a79224572064ee9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} \\neq \\cfrac{3}{3} \\neq \\cfrac{-1}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Koefisien A dan C persamaan implisit kedua bidang sebanding satu sama lain, tetapi tidak sebanding dengan koefisien B. <strong>Oleh karena itu, keduanya merupakan dua bidang garis potong<\/strong> .<\/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> Tentukan posisi relatif dari 2 bidang 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-acb264b7b74aa4dc951d87efb7708a43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ 6x-3y-12z+7=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"209\" style=\"vertical-align: -4px;\"><\/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-30503eab848d5849c33533bbd31a8f0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ -2x+y+4z-5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"205\" style=\"vertical-align: -4px;\"><\/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 menentukan posisi relatif antara dua bidang, perlu diperiksa apakah koefisien persamaan kedua bidang tersebut sebanding:<\/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-8e3df6a5267721b19719d5cf5fdd6681_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6}{-2} = \\cfrac{-3}{1} =\\cfrac{-12}{4} \\neq \\cfrac{7}{-5}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"192\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Tiga parameter pertama (A, B dan C) dari persamaan kedua bidang tersebut sebanding satu sama lain tetapi tidak terhadap parameter D, oleh karena itu <strong>kedua bidang tersebut sejajar<\/strong> .<\/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> Hitung nilai parameter<\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> sehingga kedua bidang berikut sejajar: <\/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-3f76595910ed6f4bda73af19268183f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_1 : \\ x-3y+5z+3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"191\" style=\"vertical-align: -4px;\"><\/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-cafaa5f6f87852bbfc799e1de7df7438_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\pi_2 : \\ 2x-6y+az-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"201\" style=\"vertical-align: -4px;\"><\/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\"> Agar kedua bidang sejajar, koefisien A, B, dan C pada persamaannya harus proporsional. Dengan kata lain, kesetaraan berikut harus diverifikasi:<\/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-ce428f1ffcead4e478675ac0c7af7fd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{-3}{-6} = \\cfrac{5}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"100\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam kasus khusus ini, koefisien A dan B pada denah pertama adalah setengah dari koefisien pada denah kedua:<\/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-fd9f9f85f6ba71dc375ebf245b156714_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{5}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"44\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, kita perlu menyelesaikan persamaan di atas. Dan, untuk melakukan ini, kita menyilangkan dua 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-9054a7621d7ca298b229a7aa522ca31b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"1\\cdot a=5 \\cdot 2\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"83\" 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-dda10217783919119a8704d3f875327e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=10}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi nilai parameternya<\/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-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> harus sama dengan 10.<\/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 semua kemungkinan posisi relatif dua bidang (bidang kering, sejajar, atau berhimpitan). Anda juga akan menemukan bagaimana posisi relatif antara dua bidang dihitung dan, sebagai tambahan, Anda akan dapat melihat contoh dan berlatih dengan latihan yang diselesaikan. Berapakah posisi relatif dua bidang? Dalam geometri analitik, hanya ada tiga kemungkinan posisi &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/posisi-relatif-dua-bidang-dalam-ruang-r3-contoh-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Posisi relatif dua bidang dalam ruang<\/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-249","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>Posisi relatif dua bidang dalam ruang - 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\/posisi-relatif-dua-bidang-dalam-ruang-r3-contoh-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Posisi relatif dua bidang dalam ruang - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan semua kemungkinan posisi relatif dua bidang (bidang kering, sejajar, atau berhimpitan). 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