{"id":221,"date":"2023-07-11T03:30:24","date_gmt":"2023-07-11T03:30:24","guid":{"rendered":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/"},"modified":"2023-07-11T03:30:24","modified_gmt":"2023-07-11T03:30:24","slug":"rumus-persamaan-vektor-suatu-garis","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/","title":{"rendered":"Persamaan vektor garis"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan cara menghitung persamaan vektor garis. Selain itu, Anda akan dapat melihat beberapa contoh dan latihan dengan latihan yang telah diselesaikan. Dan Anda juga akan menemukan bagaimana titik-titik suatu garis diperoleh dari persamaan vektornya. <\/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-es-la-ecuacion-vectorial-de-la-recta\"><\/span> Apa persamaan vektor garis tersebut?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ingatlah bahwa definisi matematis garis adalah sekumpulan titik berurutan yang direpresentasikan dalam arah yang sama tanpa kurva atau sudut. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Jadi, <strong>persamaan vektor garis<\/strong> adalah cara untuk menyatakan garis apa pun secara matematis. Dan untuk itu yang diperlukan hanyalah sebuah titik yang termasuk dalam garis dan vektor arah garis tersebut. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcomo-se-calcula-la-ecuacion-vectorial-de-la-recta\"><\/span> Bagaimana cara menghitung persamaan vektor garis? <span class=\"ez-toc-section-end\"><\/span><\/h2>\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\"> Ya<\/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-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah vektor arah garis dan<\/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 yang berada di sebelah kanan:<\/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-798c10bf651dde568bef6722fc25cef6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (\\text{v}_1,\\text{v}_2) \\qquad P(P_1,P_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"197\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Rumus <strong>persamaan vektor garis<\/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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/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-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" 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-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> adalah koordinat kartesius dari setiap titik pada garis.<\/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-d38a31ec1eb0a45c9ee8e1b143e3b4b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_1\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"><\/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-2c78cc5579163a0956b9462599d75b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P_2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"18\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah koordinat titik yang diketahui yang merupakan bagian dari garis.<\/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-16a61eafb9e0a7b88b98a7fffd74c09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_1\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"15\" style=\"vertical-align: -3px;\"><\/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-43a68c72834dd1643b28f72554b27956_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\text{v}_2\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> adalah komponen vektor arah garis.<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah skalar (bilangan real) yang nilainya bergantung pada setiap titik pada garis. <\/li>\n<\/ul>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\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-de-la-droite-1.webp\" alt=\"persamaan vektor garis 4 yang\" class=\"wp-image-1304\" width=\"281\" height=\"268\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Ini adalah persamaan vektor garis pada bidang, yaitu ketika bekerja dengan titik dan vektor 2 koordinat (dalam R2). Namun, jika kita melakukan perhitungan dalam ruang (dalam R3), kita harus menambahkan komponen tambahan pada persamaan 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-3ef53596406b2fe36258a0421c91336b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y,z)=(P_1,P_2,P_3)+t\\cdot (\\text{v}_1,\\text{v}_2,\\text{v}_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"288\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Di sisi lain, perlu diingat bahwa selain persamaan vektor, ada cara lain untuk menyatakan garis secara analitis: persamaan parametrik, persamaan kontinu, persamaan implisit (atau umum), persamaan eksplisit, dan persamaan titik-kemiringan suatu garis. . Anda dapat melihat semua <a href=\"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/\">jenis persamaan pada baris<\/a> di tautan ini. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-hallar-la-ecuacion-vectorial-de-la-recta\"><\/span> Contoh cara mencari persamaan vektor 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-109\"><\/div>\n<\/div>\n<p> Mari kita lihat bagaimana persamaan vektor garis ditentukan dengan menggunakan contoh:<\/p>\n<ul>\n<li> Tuliskan persamaan vektor garis 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-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> dan memiliki<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> sebagai vektor pemandu:<\/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-c4f245fcb7cc0cea584213b379d0cc63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}= (1,2) \\qquad P(3,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"160\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mencari persamaan vektor garis, 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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-d4d382959b5006597c30376b200d167f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(3,0)+t\\cdot (1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"183\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"obtener-puntos-a-partir-de-la-ecuacion-vectorial-de-la-recta\"><\/span> Mendapatkan poin dari persamaan vektor garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita menemukan persamaan vektor suatu garis, sangatlah mudah untuk menghitung titik-titik yang dilalui garis tersebut. Untuk menentukan suatu titik pada suatu garis <strong>, cukup berikan nilai pada parameternya<\/strong><\/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-50d6971192a73f12b183dbddd7c75197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{t}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dari persamaan vektor garis.<\/p>\n<p> Misalnya diberikan persamaan vektor garis 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-cd6dd1a3c3a001280f7fc7d94713c2ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(1,-1)+t\\cdot (2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"196\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sebuah poin dicetak dengan mengganti<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dengan nomor berapa pun, misalnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1723333cf1be89f8646b303471646921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-81a04a05d8ea6730567685bff8148959_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(1,-1)+1\\cdot (2,3)\\\\[2ex] &amp; =(1,-1)+(2,3) \\\\[2ex] &amp; = (1+2 \\ , -1+3) \\\\[2ex] &amp; = \\bm{(3,2)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dan kita dapat menghitung titik lain pada garis yang memberikan hal yang tidak diketahui<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> nomor yang berbeda, misalnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a6ff8890aca4d4d4f6d560faae50d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-70cfec547c993eddfea11d50bef03bae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(1,-1)+2\\cdot (2,3)\\\\[2ex] &amp; =(1,-1)+(4,6) \\\\[2ex] &amp; = (1+4 \\ , -1+6) \\\\[2ex] &amp; = \\bm{(5,5)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"199\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, kita dapat memperoleh banyak titik pada garis yang tak terhingga, karena variabelnya<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> dapat mengambil nilai tak terhingga. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-ecuacion-vectorial-de-la-recta\"><\/span> Menyelesaikan masalah persamaan vektor garis<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan persamaan vektor garis yang melalui titik 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-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> dan vektor arahnya adalah <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-80c361259467f8dee47e246c764ef897_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{\\text{v}}:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"18\" 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-b5adb01b1c1b8426314e6158a3ad6ff9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(-1,3) \\qquad \\vv{\\text{v}}=(4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"188\" 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 menghitung persamaan vektor garis, 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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-db734ce476b56a89bd305a06648b08d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(-1,3)+t\\cdot (4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/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> Hitung tiga titik yang berada pada garis dari soal sebelumnya. <\/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 memperoleh titik dari suatu garis yang dijelaskan dengan persamaan vektor, nilai parameter harus diberikan<\/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-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Persamaan vektor yang dihitung pada soal sebelumnya 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-db734ce476b56a89bd305a06648b08d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(-1,3)+t\\cdot (4,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Untuk menghitung suatu titik, kita mengganti titik yang tidak diketahui<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> misalnya oleh<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1723333cf1be89f8646b303471646921_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=1:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-36452411cca47b72db95b2876b03f69d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+1\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (4,-2) \\\\[2ex] &amp; = (-1+4 \\ , 3-2) \\\\[2ex] &amp; = \\bm{(3,1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Untuk menemukan poin kedua kami berikan<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> misalnya nilai<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-4a6ff8890aca4d4d4f6d560faae50d3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=2:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-5a5fe3c08ab62695f62cf76df97aac2e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+2\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (8,-4) \\\\[2ex] &amp; = (-1+8 \\ , 3-4) \\\\[2ex] &amp; = \\bm{(7,-1)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan terakhir, kita memperoleh poin ketiga dengan menugaskan<\/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-b4e3cbf5d4c5c6d9b702dd139f14c147_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> nilai dari<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-063c366f7c1d1f7a8a92c459c8c495d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t=3:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" 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-9710aef8527fc6c53d21109ea01a1b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned}(x,y)&amp; =(-1,3)+3\\cdot (4,-2)\\\\[2ex] &amp; =(-1,3)+ (12,-6) \\\\[2ex] &amp; = (-1+12 \\ , 3-6) \\\\[2ex] &amp; = \\bm{(11,-3)} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"145\" width=\"213\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Anda mungkin mendapatkan poin yang berbeda-beda, karena bergantung pada nilai yang Anda berikan pada 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-4998f61a094184afa02f41dd4ab518c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Namun jika Anda mengikuti prosedur yang sama, semuanya baik-baik saja.<\/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> Atau dua poin:<\/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-39e1ccbebf7e7d41e0c9bc87567a83c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(5,1) \\qquad B(3,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"155\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Tentukan persamaan vektor garis yang melalui kedua titik tersebut. <\/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\"> Dalam hal ini kita tidak mempunyai vektor arah garis, kita harus mencari vektor arahnya terlebih dahulu kemudian persamaan garisnya.<\/p>\n<p class=\"has-text-align-left\"> Jadi untuk mencari vektor arah garis kita harus menghitung vektor yang ditentukan oleh dua titik tertentu:<\/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-2ef2698c8dcca35e09a5fbbb3c07bdcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}=B-A= (3,-2)- (5,1) = (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"329\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan setelah kita mengetahui vektor arah garis tersebut, kita dapat menentukan persamaan vektornya dari salah satu titik yang diberikan dan 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-16e43c9d65f7fae5b0e20a3caca1df38_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(P_1,P_2)+t\\cdot (\\text{v}_1,\\text{v}_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" 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-68960ac44d082e7f07e54f954e16ac41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(5,1)+t\\cdot (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"210\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Persamaan yang ditemukan dengan memasukkan titik lain ke dalam rumus juga valid: <\/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-a3931a59d4987a867d7e380fe782df9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(x,y)=(3,-2)+t\\cdot (-2,-3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"224\" style=\"vertical-align: -5px;\"><\/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 cara menghitung persamaan vektor garis. Selain itu, Anda akan dapat melihat beberapa contoh dan latihan dengan latihan yang telah diselesaikan. Dan Anda juga akan menemukan bagaimana titik-titik suatu garis diperoleh dari persamaan vektornya. Apa persamaan vektor garis tersebut? Ingatlah bahwa definisi matematis garis adalah sekumpulan titik berurutan yang direpresentasikan &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/\"> <span class=\"screen-reader-text\">Persamaan vektor garis<\/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-221","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 vektor garis - 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\/rumus-persamaan-vektor-suatu-garis\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Persamaan vektor garis - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan cara menghitung persamaan vektor garis. 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Selain itu, Anda akan dapat melihat beberapa contoh dan latihan dengan latihan yang telah diselesaikan. Dan Anda juga akan menemukan bagaimana titik-titik suatu garis diperoleh dari persamaan vektornya. Apa persamaan vektor garis tersebut? Ingatlah bahwa definisi matematis garis adalah sekumpulan titik berurutan yang direpresentasikan &hellip; Persamaan vektor garis Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/","article_published_time":"2023-07-11T03:30:24+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-391ac2e3ba0b7f327ba5a0edc1ba162d_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\/rumus-persamaan-vektor-suatu-garis\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Persamaan vektor garis","datePublished":"2023-07-11T03:30:24+00:00","dateModified":"2023-07-11T03:30:24+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/"},"wordCount":568,"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\/rumus-persamaan-vektor-suatu-garis\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/","url":"https:\/\/mathority.org\/id\/rumus-persamaan-vektor-suatu-garis\/","name":"Persamaan vektor garis - 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