{"id":311342,"date":"2023-01-23T09:09:00","date_gmt":"2023-01-23T02:09:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=311342"},"modified":"2023-02-06T10:29:02","modified_gmt":"2023-02-06T03:29:02","slug":"vektor","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/vektor\/","title":{"rendered":"Pengertian Vektor dengan Ruang Lingkup dan Contoh Soal"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full is-resized\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pair-geometry-compasses-paper-white-table_114579-76159.webp\" alt=\"\" class=\"wp-image-311344\" width=\"780\" height=\"520\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pair-geometry-compasses-paper-white-table_114579-76159.webp 740w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pair-geometry-compasses-paper-white-table_114579-76159-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/01\/pair-geometry-compasses-paper-white-table_114579-76159-263x175.webp?crop=1 263w\" sizes=\"(max-width: 780px) 100vw, 780px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, pernahkah kamu bermain tarik tambang? Permainan tarik tambang akan dimenangkan oleh tim yang memiliki kekuatan atau gaya total lebih besar. Jika gaya tarik ke kanan lebih besar daripada tarikan ke kiri, sudah pasti tim kanan akan memenangkannya. Peristiwa tarik tambang itu merupakan salah satu contoh penerapan vektor dalam kehidupan sehari-hari. Saat membahas vektor, ada beberapa rumus yang harus kamu pelajari. Lalu, apa saja rumus vektor itu? Daripada penasaran, yuk simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Pengertian Vektor<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Vektor adalah besaran yang memiliki nilai dan arah. Operasi vektor tentu berbeda dengan operasi skalar. Pada operasi skalar, kamu bisa mengoperasikan langsung suatu bilangan, misalnya 2 + 3 = 5. Namun, tidak demikian dengan vektor. Operasi vektor harus mengacu pada arah besarannya. Jika ke kanan bertanda positif, maka ke kiri harus bertanda negatif. Prinsip dasar inilah yang digunakan pada peristiwa tarik tambang.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Ruang Lingkup Vektor<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Berikut ini merupakan ruang lingkup vektor.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Vektor Negatif<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vektor negatif -P adalah vektor yang memiliki nilai sama dengan vektor P, tapi arahnya berlawanan.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Vektor Nol<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vektor nol adalah vektor yang tidak memiliki panjang dengan arah sembarang. Di dalam penulisannya, vektor nol biasa dinyatakan sebagai matriks nol seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/sHuSg3v9TaPm0x89FHnIBd2HWaV27R6QmSbAGr2Lsj1JdQ6PNq3aoRJpMid0goowi7qHQx5-RPH6xaTMK7fBQCGjGxN7P1ooE6JQYZ8C_uInSm5XSdnydaKcAQbpLREbvPSER1NLxpBjk2Y92_tD4VfMpfInY-FY1qIoaXxnsBs1KTW0H_ior4AtPQWF3uKuVEhdlq3_Pg\" alt=\"\" width=\"55\" height=\"45\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Vektor Posisi<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vektor posisi adalah vektor yang ujungnya berada di suatu titik koordinat tertentu dengan pangkal berada di titik koordinat (0, 0). Vektor posisi biasanya memuat vektor satuan <em>i <\/em>dan <em>j<\/em>. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/atNgTW1C1gQrzm_OYQj92O8MyMOdPEK6Cq3zifCha8YdXJWASU9KBxpYEWCCXiiN4aPeY8FONL84bco4W7-j3UNm1PyMm8OBlr729bP9keadsQMISTnXBA-bsaEFbP3ifzXCjLqkMfYJXbTmqZcJriS8bPoaAflT2IPB_MeAv54sCq_FZVLF--VkPhYjLBrph-78PyTQOA\" alt=\"\" width=\"283\" height=\"316\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jika ditarik dari titik pusat ke titik P, maka vektor posisinya disebut OP. Panjang vektor OP bisa dicari dengan teorema Phytagoras, seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/zLOVnjieqCzE4uVXd6o-GEJhW7tTtPqSX8IOs2dxHGu747kYp3TS2q9_yivK1FS6LvCLknQXaeZAPFCP9FqSkBs73VY0X68MQCCd_9DCmQmvYpQubdh6mmccn3XpsrV3kpNDfIRv09699vN783jMUT-mHZVq9CMnP0bXqJa6XCsWfvPIzgN2xUHiakaPnuaHboHTPykjwQ\" alt=\"\" width=\"99\" height=\"54\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, bagaimana jika titik pangkalnya tidak berada di titik (0, 0)? Perhatikan gambar berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/slqcEe6wjCjXXBeZ2HWZIAjxBVsP8cy1m_MNu3-vjL1OtmCMx7wVhrWQV077XhfK_KYML_sPH2lGz7MzBhTqy7eYNJd9zJSjajYjJoDgj7EegJLT3KTPSpdsiWqYf2PmTSEqL_WXJVcFyAj9HlfwFfGCJ8HqPuXnv5_dfoM9Ac0EUC9qSDei9D4hljdUJFg3XqfPb1B0IA\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Cara menentukan panjang vektor PQ, gunakan rumus vektor berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/hu94vc-A7m7SO8WYbaQVWkhItxwUyOS8mbUSeCLoKM5hgUwHMSjFZFISK16swRycI6R4ajzXGjrgIvLTc5zXZAdOO9N3lgP2Iiz-k1L8vgk3MgPr6S8D7l_TPbg2oz5DsaRc1PjNYtxQyxx6Gd64OX_kwcEn6bqPBb3aWCYZTvHCgujwQv2DQSVxKCppBND3b_OOBveT6Q\" alt=\"\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Panjang atau Nilai Vektor&nbsp;<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Panjang atau nilai vektor adalah nilai vektor tanpa arahnya. Panjang vektor selalu bernilai positif. Untuk itulah, penulisan panjang berada di dalam tanda mutlak |\u2026|. <strong>Rumus panjang vektor <\/strong>sama dengan rumus Phytagoras, yaitu sebagai berikut.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/nOIOIctUa6prZro2yxayaVbprWdqBKnXi5uXFqXbCGXOAN9AlFHiR_gejy-DQUYaTA0ePJeKtoP84F1soVRo2pYGEECi42CarKUm74fhFNlJKsWUfBvgyThHeUgaF3vIeMUN3fYSudqL3A3zf3LXnDwe7f9FUgUFLL8xyqAGAZ00gXezK9twJ9_I_tOMlWsiHNBKIy-Adw\" width=\"121\" height=\"41\"><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;\u2192 jika pangkalnya berada di titik O (0, 0).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/eY5kNaG_OHV1d72w9vvJMqjUGGDrcN33BpGztuOk1chGBsgm36fTYZwCASgAuKuBf48bx18EpODUlhfOLjrNeQq1cr3Py74SskgXohFcgUgQWv4DCym0wPHRS4MFUo49DcQ9TRiNxgfowjMOhy17JGLyZY4GxOUw-K31WnPxgznfKaMIuKksNMblgrKOPq5kp69z-jv2rg\" width=\"201\" height=\"49\">\u2192 jika pangkalnya berada di titik P (<em>x<\/em><sub>1<\/sub>, <em>y<\/em><sub>1<\/sub>).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Vektor Satuan&nbsp;<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vektor satuan adalah vektor yang memiliki nilai 1 satuan. Cara menentukan vektor satuan adalah membagi vektor tersebut dengan panjang vektornya. Perhatikan rumus vektor berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/m5R1si3mT5dL3nhCm9KRL0i98WUlav4TBNwSWSYxU_v-x7jdnDNoso9ASsY75St7PYydt_fa_erZ1_-lO2cHiLQkOvbR1WNlBXAWES_Nr4yP8Q_Aj7_NMor4CcZvHSPO7SFoBtEM7T2hEijo1mUdt-RBGahgEn_creV8tMv-bIwnNdVOvIPxyqOATvaO_Wn9Tiwz7BPUDQ\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Vektor pada Bangun Dua Dimensi<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Vektor pada bangun dua dimensi memiliki dua komponen, yaitu komponen vektor searah sumbu-x dan komponen vektor searah sumbu-y. Penulisan dimensi dua vektor adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/6-4CiJV5LnPW7QejcLWLqkxNYfCxh_AT9TkqAqZZe7cJ9486Qa-k38JIOVzriSZL3T1LoMIBh8DijB1oqozUQa_gkzBUN-cv_mtT419uGC5NQ8d6Eu3lQnnmgCLaG4bQOar6ZsNdBBiAvd2FGeTtj1GiYpFvUunhzMqiLvLE7GyktJ-_Sy0ltSKEKns913Xkh-n2jBJ-sg\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Operasi Vektor<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Jenis-jenis operasi vektor sama seperti operasi bilangan pada umumnya. Perbedaannya terletak pada cara mengoperasikannya karena melibatkan arah. Adapun bentuk-bentuk operasi vektor adalah sebagai berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Penjumlahan Vektor&nbsp;<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Penjumlahan dua buah vektor mengacu pada dua aturan, yaitu aturan segitiga dan jajargenjang seperti berikut.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Penjumlahan vektor dengan aturan segitiga<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Menurut aturan segitiga, penjumlahan dua buah vektor dilakukan dengan meletakkan pangkal salah satu vektor pada ujung vektor lainnya. Hasil penjumlahannya merupakan jarak antara pangkal salah satu vektor dan ujung vektor lainnya. Perhatikan contoh berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/yzlhkbJ229kUwbtn5sHZ_oT90cLsRgW6VzdUdyOC1Sgv1C3kJArDqLxniwyPZEKJh-ilRNnIHE8K0geQtiDKf-jg1nBkUTmDcL9UQdSxmilfHV-CohRG6h07QO7cZwZQOxeNt5-IuhvEUFN7JHhgquC1HPrXu5fovFduvqX1-zdS5CMhOG64MZKeZrFA5-s6GoyJQk2s3Q\" alt=\"\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Penjumlahan vektor dengan aturan jajargenjang<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Menurut aturan jajargenjang dua buah vektor bisa dijumlahkan dengan meletakkan ujung pangkal kedua vektor pada titik yang sama seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/IrQUPjzvqY3JjbBCH_u-bFmbuksmNDblxdjKSJy7qTW5qSOZ2-7FvVgn28-ljeEtzbQyml26RD4gX5-StCcQS5BDmxem5iXiAfcyy-hk31G804-gZUdgFKg5rdodmaUaa_zNPUxe1R4W9XpxOLB8U2qy_uKoMccsOQtaiEz_d71z3Qk4bnpMu6eE7x8koDqINYtO7iexMg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk P=(<em>x<\/em><em><sub>1, <\/sub><\/em><em>y<\/em><em><sub>1<\/sub><\/em>) dan Q=(<em>x<\/em><em><sub>2, <\/sub><\/em><em>y<\/em><em><sub>2<\/sub><\/em>), rumus penjumlahan dua vektornya bisa dinyatakan sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/dg-7UThRQGZRTyCFcJFd8KJg33d0zhWPKjgNVfSwUHfB2VGgQ18bnyGQzEN7ghyERsVkc-SfsagqcTC8dXQm_g3Jt3z3DudD-u-9GPYpviUcdfwUItkKxuKGjQu0w4HBPmACpIIF2Q7YN-zh-VpDCVHMcOd-gbpOsmhtOLV0RIWRdhRfTMmSEOL8zxlfcvCr8G5U3HQdWg\" alt=\"\" width=\"155\" height=\"107\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Selisih Vektor&nbsp;<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Selisih vektor adalah operasi yang digunakan pada dua vektor yang memiliki arah atau tanda yang saling berlawanan. <strong>Rumus vektor selisih <\/strong>dinyatakan sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/yYT6aAusn4uSwOJe1k237hJkvBtM9bGBZT6n62vR40d41eKl6mIX74RWIZBSYV8-UJmK3BVel7wmya5OFLDak2i5cdGPMjTvUo87h6ilBSGGHyqXufmzGH-vCRcPyi5mmdl9fCgsfO6iMQbzp6Mabc-YNOz6cXJNEIM8EAK5Jf7304M9lUGIBAnFKNl5yq0zGbsiCwaI6w\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan contoh ilustrasi berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/URzYWHXpEwfSeI7B4nigqrgQvMLeL_ROWCWq8wZRa3xrJkkMuNFXAVuXkoK6_43VZzvij_SZvx2L9c9pmVfV0z-rmVsJyF6KY4E8kw5Ayuvc_UkuRpqrBrF9qf32UxGu1o08i-hBbS6rS361gpO0nI4WvXdt8xgk9Eu8z6-L5qa5-J8IVZ1C4FEiX2bDxVQ8\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari ilustrasi di atas, coba kamu perhatikan arah vektor Q. Semula arah vektor Q ke kanan. Oleh karena berlawanan, maka arah arah vektor -Q ke kiri.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Perkalian Vektor&nbsp;<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rumus perkalian vektor<\/strong> itu bermacam-macam, tergantung dari jenis perkaliannya. Adapun jenis-jenis perkalian vektor itu adalah sebagai berikut.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Perkalian vektor dengan skalar<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Perkalian vektor dengan skalar artinya, skalar menjadi pengali dari vektor yang dimaksud. Misalnya, vektor P dikali skalar <em>m<\/em>, maka vektor hasil kalinya memiliki panjang <em>m<\/em> kali panjang vektor P. Untuk arahnya, bergantung sepenuhnya pada <em>m<\/em>. Jika <em>m<\/em> &gt; 0, hasil kalinya searah dengan vektor P, jika <em>m<\/em> = 0 akan dihasilkan vektor nol, jika <em>m<\/em> &lt; 0, hasil kalinya berlawanan dengan arah vektor P. <strong>Rumus perkalian vektor <\/strong>dengan skalar adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/zWNEqerjf0xI_xpyztX90BI88VYIbl4q7zRjWwS2gtbI-f5FOpzkRWcIv9IyOd6AaZUy7tSg2yNcOO8VtymklnaMYpOjP73Q9TbtT_8ubc0nBbrdW13Gwbo7C4gCax29GEpA-x_iYyDlp7iOaMd8oOyYVH5igFxQ7IaFtR1nKm5s4LhB1iVTnQbZZYoNkCiPNyaa8-PYIg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Perhatikan contoh berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui <sub><\/sub>. Tentukan nilai dari 2 \u2219 P!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/hJfgbLyMe9u0JJ0ibgm_VFKfe7Xjr-mH07-YGnNb1ctvXatbcdEbOeNtj5Q9Vgqz-8nsGC2Tx3mBIEtlJLwJbDD-n4FqCeBTaA3hO1Y3qVRsVq8MX8HL_5XFt4r_KMh4MxicGUQemroUrzcivTYPfmzYigaToxoxbYK3yWxoajh8v8SivECk6w8pMRBZoWsIbndhskXDFg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai 2 \u2219 P = 4 -10 .<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Perkalian vektor dengan sudut tidak diketahui<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Pada prinsipnya, rumus perkalian titik antara dua buah vektor memiliki cara yang sama seperti perkalian pada umumnya. <strong>Rumus perkalian antara vektor<\/strong> P=(<em>x<sub>1, <\/sub>y<sub>1<\/sub><\/em>) dan vektor Q=(<em>x<sub>2, <\/sub>y<sub>2<\/sub><\/em>) adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/nw56zGRv6C_tcDs6K9iGslGM5yfXGeCrCkBdIpUkKf72QRG4PvbmiujTHx_dNg25c3pR6xUOCpOdgNumwL2SjnBRTMDhlLgotsUplSNrgv5hYeFSSf5y2K8axNPamqihSpzN7SJt3HRO2-QcS0uXnXS7aGP-XQSIrV-5ZzkdktyemUVFbPQXf-YpjxLBaBdieLpkyBmgLA\" alt=\"\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Perkalian vektor dengan sudut diketahui<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Jika posisi dua buah vektor membentuk sudut tertentu, maka rumus perkaliannya adalah sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/QszIt20jrkNYQXIolUarnmBbRu_ychsPruoT5hAXe_ye7OPYRLs4qQIq7y8XHFW8EQ1Ti5E2rm9opDvss2ai-NE2cz_Ep_w_io0Mwzp-4oudC9BswltueGNou3cxZAB_XWnbpDV80WjiUhUV1hXTFJIWR0OGO4yXtrUKad9__HdD7tA3M5NmM5G7kwD_G8aG17js6Hn2rw\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/afmlZ2N2Fin8xonFXAxk0VK-u17tHWktQYOkk8bZZUzj-WYTkB3V75p-Jvepcp4_vmGyewzvVj5GqBiKB7Y9fIXlIeXN2tzUjG1eyknUaC2dbcdYBk3ndpA1QVwh7ncBzJXGhNhA610O2gFXYgf_nBZNGHL5cXF4Nxkw4QINBtIMlV_Vvc7TcQOc5GSqp11e05EJYLl2Cw\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1 = sudut yang dibentuk oleh vektor P dan Q<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari nilai cos \u03b1, gunakan rumus berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/4gRMq9RTFyxF2vg81QpOmRiiwOcmSRSdqIKKueUeVA5uzb7xwOEUJ7Knp8HLfLwpw0PClEuCjznGwd31BsW0TFYzVN0av_QM2sD2wOWdPFCxTtsruKGSaH3XN9Zkq16OcdezIBhvxeHBtZxqnyddXHp6QDi5VoVATo_4wGWPOu44gm3or1ZtZQubUqYkMW6dLtTvuD7WuQ\" alt=\"\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Resultan Vektor<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Resultan vektor adalah panjang dari suatu vektor. Perhatikan gambar berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/DFf8vi6Y7b8zIgPrVG0F0kqL6lOJBDDrFK5hccXDmLsYeNcnUTSmXcyXA30O3z-CVEYhYaiduF8UvUhSAmXz06hszICw1M8LBcrBJivVyD4x_ketXucJjFcMWp4Y712IIB_eP1Q9KTsO_h_ns-qDFP1Hsw4v5U-NOhhhFk8_i1zCe0D45HLiN3MeAh2m4sraBarN47xYmA\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari resultan vektor atau panjang OR, gunakan rumus berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/ZIL-f5jsVmg7xa5MUzNSDU_vowssmhf-blt4ARVo5ZutuhROE8Y4FrV5S4njEftaEQgejNlDYCYYbb8EV0zic0zyvOA-huD-h5P2Eo8KNxQC13rIaduFZo_9Y3zTdLtVNzdGvUg2TGYjLk1XH7CG5ljvthg7O4S_vdvE14FW-X0V8L5j95EqBuM0eETYAQLiw4fQSVRrew\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sementara itu, arah vektor resultannya bisa ditentukan dengan rumus berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/wDxeEI0nX8lz_2ConDmwq9VH9G5JmzlkdBqmyTdz_kIkn8gRWEvhy4LNDYhI8j50Q14Hm0ErkwYmEoCkTzQSnf2Fyr1FpCGhdSAO1BCF1OMSxxGp_n1H47FOqPgRPYo5cVO65xBOa2MNPn80RX1rLfjTaTvujgdwP_dA-VOGR2hJjP0MJZONuBecTNF8NpjhBXRWbUajLA\" alt=\"\" width=\"146\" height=\"47\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh Soal Vektor<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Setelah kamu tahu apa saja rumus-rumus vektor itu, yuk asah kemampuanmu dengan contoh soal berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal 1&nbsp;<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dua buah vektor berada pada posisi seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/MvcO2c55v42UwzPTsYVVGPNEFvbSU42HZ0SDG5EzNmmuBcV1MqfMMfcsLiaiqXGQGxt9sofPywQUZ6aARohxn5DsxZdva5zWOqfr9zBokbtfPPOf2Fu3AkFf0wChLuyaPy7rZeUYmMi-zUbpQuQA5CiTqotZJ_B6c75zrMr2JirlTT9eahquj3b-a3UawLPBdMqeivK8pw\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentukan hasil kali antara A dan B!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Oleh karena kedua vektor membentuk sudut, kamu bisa menentukan hasil kalinya dengan rumus berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/nkrG1CcL1emjh4ESwjc89S67cmT7tSenINiZG1VS4Cm7JcXAVmoWdm13ubEMHhZ8ARvQfwWVZUPXTmeVYm0D3K_JynzXIT-5BaHBkEK-hkduLVn-xdf-PhpY1_3hRM1lN1b8p0q6qYPgIm2qcomfpxyY3he2r9Z2OzppdFD9xOq8jqmfmyYrqzjXAosqT9nXLD841fEemg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, tentukan dahulu |A| dan |B|.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/zmqzuOVu4uJ8aanshJwZloHY5ZpwMhqNEHkAe96VYdTn-fDchlV6o8Nq2FnYnPj2brqROa6bBXWxlbt9mpiSb78BhnIua98Ptf9fDIIYsAth0mTjzoz4nCvJhdSFt-2ACK6Bu1e_WTEq0qUXtWAJ3HahXyTif0BdShDVx-v0L_HXBCSlc0N6CFKCTJ8sFiElim8OYPR_kQ\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, substitusikan pada persamaan tersebut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/U_vfVhscyA-ObFyfkFNk-kRYZ0maAQ5OwyedOtGKWRn11wnPydaCi7RBOQAT11hn6_y6pgDTG19kTcNa0lyS-2NZRMDwtazMERUR-7NEne5rw2hNMMAt1_vxJK5HkZvamwalSmqJ-styjD8JgVUxnZ0Sq52vzDOVOaMDK8Ohry7AjFa2DWr6QkqpyC5W9vCk6z6jaq38uQ\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, hasil kali antara A dan B adalah 9,87.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal 2<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua vektor berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/V4aXpFSQskYfaMR4BbPXjT2PUO50VigJbKJG_dE8JyNYWyVNXviqZZZ_KP_mQQZLHRyRslDuvcyDzIMMGwqC03dq8hk9JIo_fjmemdWz5S15PzN_rGHdEeZOuBVlY2w3eVVeLHHmE7HAX0mbcSCcLCjXtAq6RxMwesRxZd5fuDadG_HVpJYy__L5lqmH14OioqDnhgbRyg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Berapakah nilai cosinus sudut yang dibentuk oleh kedua vektor?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Langkah pertama, kamu harus menentukan panjang vektor&nbsp; p dan q.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/8a_Bs5D5T09jiqVpm0reb3EGx1gDYji29_LSP0KlbyrtBseyaDbccR2pAKJpkGVLbPhTMe-0YJNqkl99KW5Pm_lTN6WqeCuiHW5sqjLi5EYeuO2C9tS67Wljq2dDBRt4zCqtLSIuP7YHXPXvUUSHmVSw0f2cUhVH6JLxO4HYwwc8qVuPTa-x9eOsanUKbSLWxjE_oRq9Fg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, gunakan persamaan berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/jsj00ORnK-g-8JJI5_2HKMUwZExKq67Ir-smYJP1qPucN7gbxBfaWn5kWoMCXyjcH-0JWX60nAW0rtf0G-C4LepNQZLDoyvL0JjNS6UJfDR69sgURmB3-UlYwgiZHyVyV-SJdadjBH-hpiQsCRuJqwwxyyDjCsGEZ0n0l3xIrogLRts-BkG9y_hDNXOMh9dVZ2xnOGgvow\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai cosinus yang dibentuk oleh kedua vektor adalah 865.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Contoh Soal 3<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sebuah batu besar berada di tengah lapangan. Untuk memindahkan batu tersebut, dibutuhkan 2 truk penarik dengan posisi seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Sxgj5dMw4F-aa7GDrIC26B5NJr-LtUg8Iy2AU9dqAlskX587GvwZNUDDrS8T4z21zu824bmIfNDCb9Geo1c0DMgn9eCrSZtmhCT8wV_BMfwpDCkR6RzE15Jk1ATGuAu3bCT3R2SSkcOjmhzXlBvj_DW4PFmm2dUWo-38IEd9za11SYdMW-jDKrFYshreFCzwdwRg1u0LXg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Berapakah resultan gaya yang dihasilkan oleh kedua truk penarik?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>F<\/em><sub>A<\/sub> = 120 N<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>F<\/em><sub>B<\/sub> = 150 N<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u03b1 = 30<sup>o<\/sup><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: <em>F<\/em><em><sub>R<\/sub><\/em> =\u2026?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawab:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk menentukan resultan gaya kedua truk, gunakan persamaan berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/rFQ47zfEy-pb2DZt7lFAcfNB4taDXwkjvJywkaE9UFDrPrU3Y-OVvn5Nwd0OAiWfaYubeJBVHzNchc9KsIvsJ0vByP8fJZpujxoI6tgG2hrttSofTJUGB8amKiPiJOma252kkXhKkk9g4UChwBWd1f5KQJh3rIoqVCmBbGMR2iRsnUdx3Yx2UaU0-IQMz8QWfb1mcq8Tgg\" alt=\"\" width=\"268\" height=\"109\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, resultan gaya tarik kedua truk adalah 234,30 N.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, pernahkah kamu bermain tarik tambang? Permainan tarik tambang akan dimenangkan oleh tim yang memiliki kekuatan atau gaya total lebih besar. Jika gaya&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":311344,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384865],"tags":[679386731],"ppma_author":[679386823,679386836],"class_list":["post-311342","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-materi-matematika-kelas-10"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Pengertian Vektor dengan Ruang Lingkup dan Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Kuasai materi vektor dan rumus-rumusnya di artikel ini. 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