{"id":256,"date":"2023-07-10T08:56:34","date_gmt":"2023-07-10T08:56:34","guid":{"rendered":"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/"},"modified":"2023-07-10T08:56:34","modified_gmt":"2023-07-10T08:56:34","slug":"jarak-antara-dua-garis-dalam-ruang-di-r3","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/","title":{"rendered":"Jarak antara dua garis dalam ruang (dalam r3)"},"content":{"rendered":"<p>Di halaman ini, Anda akan mengetahui cara menghitung jarak antara dua garis dalam ruang (dalam R3), apa pun jenisnya (garis sejajar, garis potong, berimpit, garis potong, tegak lurus, dll.). Selain itu, Anda akan dapat melihat contoh dan 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=\"como-calcular-la-distancia-entre-dos-rectas\"><\/span> Cara menghitung jarak antara dua garis <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> Jarak antara dua garis adalah jarak minimum antara suatu titik pada satu garis dan titik mana pun pada garis lainnya. Jarak ini sama dengan panjang ruas garis yang berpindah dari satu garis ke garis lainnya dan sekaligus tegak lurus terhadap kedua garis tersebut. <\/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\/distance-entre-deux-lignes-dans-lespace-2.webp\" alt=\"jarak antara dua garis dalam ruang (dalam R3)\" class=\"wp-image-3056\" width=\"387\" height=\"297\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Jadi, mencari jarak antara dua garis berbeda dalam ruang tiga dimensi (3D) bergantung pada posisi relatif di antara keduanya:<\/p>\n<ul>\n<li> Jika kedua garis tersebut <strong>berimpit<\/strong> atau <strong>berpotongan<\/strong> , maka jarak kedua garis tersebut adalah nol, karena keduanya berpotongan (setidaknya) di satu titik.<\/li>\n<li> Jika kedua garis <strong>sejajar<\/strong> , kita perlu mengambil titik mana pun pada salah satu garis dan menghitung jarak antara titik tersebut dan garis lainnya (di bawah ini Anda memiliki contoh cara melakukannya).<\/li>\n<li> Jika dua garis <strong>berpotongan<\/strong> dalam ruang, kita perlu menerapkan rumus jarak antara dua garis yang berpotongan (lihat penjelasan detailnya di bawah).<\/li>\n<\/ul>\n<p> Jadi, untuk menghitung jarak antara dua garis, pertama-tama Anda harus mengetahui jenis garisnya dan kemudian, tergantung kasusnya, gunakan satu rumus atau lainnya. Oleh karena itu, penting bagi Anda untuk menguasai <a href=\"https:\/\/mathority.org\/id\/posisi-relatif-dua-garis-dalam-ruang-r3-contoh-soal-yang-diselesaikan\/\">cara mencari posisi relatif dua garis dalam ruang<\/a> sebelum melanjutkan, namun jika Anda tidak ingat cara melakukannya di tautan, Anda akan melihat penjelasan yang sangat lengkap serta contoh dan latihan yang diselesaikan. selangkah demi selangkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hallar-la-distancia-entre-dos-rectas-paralelas-en-el-espacio\"><\/span> Cara mencari jarak antara dua garis sejajar dalam ruang <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<p> Menghitung jarak antara dua garis sejajar dalam ruang (di R3) dilakukan dengan cara yang sama seperti di bidang (di R2): <strong>Anda harus mengambil sebuah titik di salah satu dari dua garis tersebut dan mencari jarak titik tersebut di garis lainnya. garis.<\/strong> <\/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\/distance-entre-un-point-et-une-ligne-en-ligne.webp\" alt=\"jarak antara dua garis sejajar dalam ruang\" class=\"wp-image-1960\" width=\"425\" height=\"361\" srcset=\"\" sizes=\"auto, \"><\/figure>\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\"> Jadi, rumus menghitung jarak suatu titik ke garis 3 dimensi (yang digunakan untuk menentukan jarak antara dua garis sejajar) 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-7c7a838a254403e912767fb131474703_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(s,r)=d(P,r)=\\cfrac{\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"225\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p style=\"text-align:left; margin-bottom:4px\"> Emas:<\/p>\n<ul>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-74f213a2a0ca1a22659ce06a80bc5d07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}}_r \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah besarnya vektor arah garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-aa03a29f511592c1a1ecc8b306b0cf0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2c758bec4c272382411b95fc0e7ee250_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Q\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"14\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah sebuah titik pada garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42ca8c420951296e93092e708435813a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-650eb7688af6737ac325425b5c9a5982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> suatu titik pada garis tersebut<\/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> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdca087897cc5ad573be7ce2b595dfb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\"><\/p>\n<p> vektor yang ditentukan oleh dua titik<\/li>\n<li>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-de23c83cb189398d246990817a7e83db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah besarnya perkalian silang antar vektor<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fdca087897cc5ad573be7ce2b595dfb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"28\" style=\"vertical-align: -4px;\"><\/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-50f32076ae1ee85f5b7c5a6d43a03089_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}_r\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/p>\n<\/li>\n<\/ul>\n<\/div>\n<p> Sebagai contoh, kita akan menyelesaikan soal jarak antara 2 garis sejajar dalam ruang:<\/p>\n<ul>\n<li> Berapa jarak antara dua garis sejajar berikut? <\/li>\n<\/ul>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-43cb370e9b16d006262ec6893e02dc92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ (x,y,z) = (2,1,1) + t(-1,3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"264\" 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-48307ac3d4d0b23d6816a7473b6b1c0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\ (x,y,z) = (-2,4,1) + t(2,-6,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"292\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Kedua garis tersebut dinyatakan dalam bentuk persamaan vektor, sehingga kita dapat dengan mudah mengetahui vektor arah dan titik dari masing-masing garis tersebut:<\/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-91c721e906a848c6c129721fe7908112_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r : \\ \\begin{cases}\\vv{\\text{v}}_r=(-1,3,2) \\\\[1.7ex] Q(2,1,1) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases}\\vv{\\text{v}}_s=(2,-6,-4) \\\\[1.7ex] P(-2,4,1) \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"417\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Jika Anda ragu tentang cara menentukan vektor arah dan titik suatu garis, kami sarankan Anda menyimak penjelasan <a href=\"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/\">persamaan garis<\/a> . Di sana kami menjelaskannya untuk semua persamaan garis, karena mencari vektor arah dan titik yang termasuk dalam suatu garis bergantung pada jenis persamaan yang menyatakan garis tersebut.<\/p>\n<p> Sekarang, untuk mencari jarak antara dua garis sejajar, kita perlu menerapkan rumus jarak titik ke 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-7c7a838a254403e912767fb131474703_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(s,r)=d(P,r)=\\cfrac{\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"225\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Jadi di satu sisi kita menghitung modul vektor yang dihasilkan dari perkalian vektor. Jika Anda ragu tentang cara menghitungnya, Anda dapat melihat <a href=\"https:\/\/mathority.org\/id\/perkalian-silang-dua-vektor-contoh-rumus-silang-latihan-yang-diselesaikan\/\">rumus perkalian vektor<\/a> , di mana, selain itu, Anda akan dapat melihat contoh dan menyelesaikan latihan operasi antar vektor ini. <\/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-dadf92e90a88ce334cf34bce072e5457_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP} = Q - P = (2,1,1)-(-2,4,1) = (4,-3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"365\" 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-f166cb84d794adae8b8e5678790a5ad8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{QP} \\times \\vv{\\text{v}}_r  =\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k}  \\\\[1.1ex] 4&amp;-3&amp;0 \\\\[1.1ex] -1&amp;3&amp;2 \\end{vmatrix}=-6\\vv{i} -8\\vv{j}+9\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"316\" 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-bcf2fce752d73d75254674158d4824b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\vv{QP} \\times \\vv{\\text{v}}_r \\right| =\\sqrt{(-6)^2+(-8)^2+9^2} = \\sqrt{36+64+81} = \\sqrt{181}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"464\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Dan sebaliknya, kita mencari besar vektor garis tersebut<\/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-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" 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-beb8af5ebd61faa6a707fabf3a13de60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{v}}_r \\rvert = \\sqrt{(-1)^2+3^2+2^2} = \\sqrt{1+9+4} = \\sqrt{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"351\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p> Terakhir, kita substitusikan nilai setiap suku ke dalam rumus dan hitung jarak antar 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-dfc98500cdf36f3b5f09c525579f7f9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(s,r)=d(P,r)=\\cfrac{\\lvert \\vv{QP} \\times \\vv{\\text{v}}_r \\rvert}{\\lvert \\vv{\\text{v}}_r \\rvert}=\\cfrac{\\sqrt{181}}{\\sqrt{14}} = \\bm{3,60}\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"350\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Jadi, jarak kedua garis tersebut adalah 3,60 satuan. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-determinar-la-distancia-entre-dos-rectas-que-se-cruzan-en-el-espacio\"><\/span> Cara menentukan jarak antara dua garis yang berpotongan dalam ruang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Seperti yang sudah kita lihat di awal, cara menentukan jarak antara dua garis yang berpotongan berbeda dengan cara menentukan jarak antara garis sejajar. <\/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\/lignes-dintersection-1.webp\" alt=\"jarak antara garis bersilang dalam ruang\" class=\"wp-image-2692\" width=\"226\" height=\"221\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Oleh karena itu, ada beberapa cara untuk menentukan jarak antara dua garis yang berpotongan dalam ruang. Pada halaman ini kami hanya akan menjelaskan satu prosedur, yang paling sederhana, karena dua metode lainnya lebih panjang dan rumit, bahkan praktis tidak digunakan. <\/p>\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\"> Misalkan vektor arah dan titik mana pun pada dua garis yang berpotongan 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-569f8d554a0f3704d247862d0b8ef852_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} \\\\[2ex] A\\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}} \\\\[2ex] B\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"210\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong>Rumus jarak antara dua garis yang berpotongan<\/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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/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-dbc3e38427d29b2f4444ea732f955500_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah nilai mutlak hasil kali campuran vektor-vektor tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4b6be5a59bbf478047e4f3ace338ee48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}}, \\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: -4px;\"><\/p>\n<p> dan vektor yang ditentukan oleh titik-titik<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-25b206f25506e6d6f46be832f7119ffa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"13\" 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-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\"><\/p>\n<p> . Dan di sisi lain,<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a151f35eca7cc81494de906050e773fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"><\/p>\n<p> adalah amplitudo perkalian silang antara vektor arah dari dua garis yang bersilangan.<\/p>\n<\/div>\n<p> Agar Anda dapat mengetahui cara menentukan jarak antara dua garis yang bersilangan, kita akan menyelesaikan soal sebagai contoh:<\/p>\n<ul>\n<li> Berapa jarak antara dua garis berpotongan berikutnya?<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-6c4b9507f6e33691e0b89d18dac941cd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\  \\cfrac{x-1}{2} = \\cfrac{y-2}{4} = \\cfrac{z+2}{-1}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/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-c6dac5d90c57534aa97625685e0d60fa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s: \\  \\cfrac{x-3}{1} = \\cfrac{y+1}{3} = \\cfrac{z-1}{-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"203\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Pertama, kita perlu mengidentifikasi vektor arah dan titik pada setiap garis. Kedua garis tersebut dinyatakan dalam bentuk persamaan kontinu, oleh karena itu:<\/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-8b990f78d0263975304586abbd330167_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} \\vv{\\text{u}} =(2,4,-1) \\\\[2ex] A(1,2,-2) \\end{cases} \\qquad \\qquad s: \\ \\begin{cases} \\vv{\\text{v}}=(1,3,-2) \\\\[2ex] B(3,-1,1)\\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"389\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan sekarang kita terapkan rumus jarak antara dua garis yang berpotongan:<\/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-c613737cb66f811b123f886afd479e0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"158\" style=\"vertical-align: -17px;\"><\/p>\n<\/p>\n<p> Di satu sisi kita menyelesaikan produk campuran (atau produk skalar rangkap tiga):<\/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-3238f24b114cb49bf33dd66bccad1ef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (3,-1,1) - (1,2,-2) = (2,-3,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"379\" 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-c52c12945d04e320e688caf714569113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right| =\\left| \\begin{vmatrix} 2&amp;4&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-2 \\\\[1.1ex] 2&amp;-3&amp;3 \\end{vmatrix}\\right| = \\left| -13 \\right| =13\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"321\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan, di sisi lain, kita menemukan modul perkalian silang (atau perkalian silang):<\/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-71afa7d4b49e542300c12b5263858665_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{u}} \\times \\vv{\\text{v}} =\\begin{vmatrix} \\vv{i}&amp; \\vv{j}&amp; \\vv{k} \\\\[1.1ex] 2&amp;4&amp;-1 \\\\[1.1ex] 1&amp;3&amp;-2 \\end{vmatrix}=-5\\vv{i} +3\\vv{j}+2\\vv{k}\" title=\"Rendered by QuickLaTeX.com\" height=\"86\" width=\"278\" 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-3c940dca4c85f7176555de5861b8f391_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left| \\vv{\\text{u}} \\times \\vv{\\text{v}} \\right| =\\sqrt{5^2+3^2+2^2} = \\sqrt{25+9+4} = \\sqrt{38}\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"354\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Terakhir, kita substitusikan nilai setiap suku ke dalam rumus jarak antara dua garis yang bersilangan:<\/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-b0aac39997c35738e8e84a29ff7c97c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(r,s)=\\cfrac{\\left|\\left[\\vv{\\text{u}},\\vv{\\text{v}},\\vv{AB}\\right]\\right|}{\\lvert \\vv{\\text{u}} \\times \\vv{\\text{v}} \\rvert} = \\cfrac{13}{\\sqrt{38}}= \\bm{2,11}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"273\" style=\"vertical-align: -17px;\"><\/p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini, Anda akan mengetahui cara menghitung jarak antara dua garis dalam ruang (dalam R3), apa pun jenisnya (garis sejajar, garis potong, berimpit, garis potong, tegak lurus, dll.). Selain itu, Anda akan dapat melihat contoh dan latihan yang diselesaikan langkah demi langkah. Cara menghitung jarak antara dua garis Jarak antara dua garis adalah jarak &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\"> <span class=\"screen-reader-text\">Jarak antara dua garis dalam ruang (dalam r3)<\/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-256","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>Jarak antara dua garis dalam ruang (dalam R3) - 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\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jarak antara dua garis dalam ruang (dalam R3) - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini, Anda akan mengetahui cara menghitung jarak antara dua garis dalam ruang (dalam R3), apa pun jenisnya (garis sejajar, garis potong, berimpit, garis potong, tegak lurus, dll.). Selain itu, Anda akan dapat melihat contoh dan latihan yang diselesaikan langkah demi langkah. Cara menghitung jarak antara dua garis Jarak antara dua garis adalah jarak &hellip; Jarak antara dua garis dalam ruang (dalam r3) Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T08:56:34+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/distance-entre-deux-lignes-dans-lespace-2.webp\" \/>\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=\"4 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Jarak antara dua garis dalam ruang (dalam r3)\",\"datePublished\":\"2023-07-10T08:56:34+00:00\",\"dateModified\":\"2023-07-10T08:56:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\"},\"wordCount\":752,\"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\/jarak-antara-dua-garis-dalam-ruang-di-r3\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\",\"url\":\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-dalam-ruang-di-r3\/\",\"name\":\"Jarak antara dua garis dalam ruang (dalam R3) - 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