{"id":2669,"date":"2021-04-14T09:00:00","date_gmt":"2021-04-14T12:00:00","guid":{"rendered":"https:\/\/professorpinguim.com.br\/blog\/?p=2669"},"modified":"2023-08-06T21:18:32","modified_gmt":"2023-08-07T00:18:32","slug":"versores-conceitos-exemplos-e-exercicios","status":"publish","type":"post","link":"https:\/\/professorpinguim.com.br\/blog\/versores-conceitos-exemplos-e-exercicios\/","title":{"rendered":"Versores: conceitos, exemplos e exerc\u00edcios"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Conceito de versores<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Versores s\u00e3o vetores de m\u00f3dulo unit\u00e1rio. Eles servem para escrevermos a equa\u00e7\u00e3o de outros vetores em fun\u00e7\u00e3o deles. Da mesma maneira que os vetores, os versores possuem tr\u00eas dire\u00e7\u00f5es diferentes no plano. Vamos dar uma olhada em exemplos para que possamos entender melhor.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos l\u00e1!<\/p>\n\n\n\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Exemplos de versores<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Abaixo temos os versores <strong>i<\/strong> e <strong>j<\/strong>, que vamos usar para descrever o vetor A.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/tLJLLQxoDH-9xVhqXrPxY16ebINXt_hflRO3Aj_imblNuatHRe0MczHbTVy6srjL2zxWaIev9zxQj69IuV7HfVgnRtH1cQbKWKjp7AC8PY45lkeoOl6IFdRm019oFfrKpFlzz47qI93B23-L029eLA\" alt=\"\" width=\"272\" height=\"298\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Neste caso, podemos dizer que o vetor A \u00e9 a soma de dois outros vetores: um horizontal e outro vertical:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/I1Sq4mj1SU8YC8r7_yjZBtgR8Wqt1yy4HatdHyHeiDqGBtTluzwQmHrnkbijH5xRQZLLt4o8S4Qy1k5NOqSs9KGJLVKnLmCCNl6TKzYkLy8VPaVCaRklrKaBV6Zcb6KYJexemq8pI0efI4DYI_T7ng\" alt=\"\" width=\"127\" height=\"105\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, se temos o versor i apontando para a direita e ele vale 1, o vetor componente de A que aponta para a direita vale 2.<strong>i<\/strong>. Da mesma forma, se <strong>j<\/strong> aponta para cima e vale 1, ent\u00e3o o vetor componente de A que aponta para cima vale 3.<strong>j<\/strong>.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, temos a seguinte equa\u00e7\u00e3o:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/MBhq1p3v12fOxz-JA0RkDOjYH8Tw0M47_gk2gBAGjJa3XGN6HDxzhtOcYsiSrv1j6ejm3z_FkHTmOZdbho79IW0QQfJRhCGyTy2IJdGqxNYdGNp6-ENPtC1FWyvIhCAuHZXMb5TEFPnXwEzj74sLpA\" alt=\"\" width=\"102\" height=\"28\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">se voc\u00ea quiser calcular qual \u00e9 o m\u00f3dulo de A, voc\u00ea j\u00e1 nem precisa mais do desenho; voc\u00ea vai pegar os n\u00fameros&nbsp; 2.<strong>i<\/strong> e 3.<strong>j<\/strong>&nbsp; e vai aplicar Teorema de Pit\u00e1goras, pois A \u00e9 a hipotenusa do tri\u00e2ngulo formado, assim como 2.<strong>i<\/strong> e 3.<strong>j<\/strong> s\u00e3o os catetos desse tri\u00e2ngulo.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u00b2 = 2i\u00b2 + 3j\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u00b2 = 2\u00b2 + 3\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u00b2 = 4 + 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A\u00b2 = 13<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|A| = \u221a13<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, o m\u00f3dulo dele \u00e9 \u221a13<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo 2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vejamos agora o seguinte vetor:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/NBi5DRkdcanwjdTGMrR5UAieraVVBMuhV-akTE517GddJcP56rafRACoew4igRXBMLtgG4VJF2aRwJLYsAJrg3ihYKHjSReISkFjwW60psAVWhcLYB2hfM97A6__h1tSE10jxFOalksdgPOuc4qHtg\" alt=\"\" width=\"121\" height=\"73\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Observe que esse vetor n\u00e3o tem componente j, apenas i, ent\u00e3o a f\u00f3rmula fica<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/GvntXe5TxjKWwLG_hP55Q-WlG-UPpnT7-GYNkEy3LHKDN6WFjxBEfWbDY51kwNAG5jgtsMx6hpJbHrrp2j2V7yG30-kOMoPov0czCvi_nkjYLJ-StinLCwmH8oCzEu_ueVeGQQvNrol5Ulhrvt_hKA\" alt=\"\" width=\"82\" height=\"25\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Como i = 1, ent\u00e3o:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|B| = 4<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo 3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vejamos agora o vetor C:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/vaDYka3pfJpSJyZaPvA3v9qWUEvA43B8uyjlhJiXA_esBxfhYd0Xcmx8OYsXNsOwGRSMFs2vDotSxezjQTLtLffu1alLFlkckEdwrbkrE2XPUih2zCzwrrzpuG5qRsd5TtLI3lS7Z9ET37IeKN9Kvw\" alt=\"\" width=\"153\" height=\"101\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ele n\u00e3o tem nenhum componente na horizontal, ent\u00e3o ele n\u00e3o tem nada de i. Como o vetor est\u00e1 apontando para baixo, ent\u00e3o usaremos o sinal negativo em frente a j. Logo:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/E-XNnwUpCDamb-Mgq1c24Vobu4iDXx27XDj7WKcdIVWei7-p6cm01T0XGVLAa_tngaMrNyNjsP8cpBt8TvDnh51xk7HWq3rBKeASI1tkZgi8kkYooMeHhWmW_oo_-O7UaPdlc7nMgbppKXcHOjnOZw\" alt=\"\" width=\"98\" height=\"26\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">C = -4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|C| = 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como o vetor C e o vetor B possuem o mesmo n\u00famero de unidades, podemos dizer que&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|C| = |B|.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo 4<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Vamos ver mais um vetor, desta vez o D:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/BzO_x8QvLc03U7ZCK1QOuisorQUoqE52irLRWEB9PIeR7hJ8E9xKMFAj0T1iWX6qxybrob3DQDxtY--hPLHzQlndZza1rfuTz5KY-TCVFwraTyCe7fALn5_dkfdNMTJfeCJ9fEAcUbyyMDRCiEBrKA\" alt=\"\" width=\"143\" height=\"138\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pela regra do pol\u00edgono, temos:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/mSSwFjfGcxVQSfrl5NZKQf7PDJxgpa68yX0X3Ff-iEF1W_ue_pe1_sNMq5Mkqkem3aAcpkZf5KJD336Kyr8SDAZn61sbF5QGjsHxxSnJkU17yVUmgNIgDm7I0tFSq0CMyVihrc4AnswFiyoN0cTfbg\" alt=\"\" width=\"180\" height=\"141\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">O componente horizontal de D \u00e9 igual a 3i, enquanto o componente vertical \u00e9 igual a -4j. Ent\u00e3o a equa\u00e7\u00e3o do vetor D fica:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/kRGEslE4Dk4zv1UrnesTvE3uH4xAxud3_-gZkO8OI6gL_6c32SaBzO0qdw953eb_y868CCCK8GXYQ5bI9zot4ugIfb3skT_k2zOGUDEPs0lBCAoNKcmWD3BCl5G3X4yO8-ZH-JCJRj18_z9e0M2uWw\" alt=\"\" width=\"96\" height=\"26\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hora de aplicar Pit\u00e1goras para descobrirmos a hipotenusa deste tri\u00e2ngulo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D\u00b2 = 3\u00b2 + 4\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D\u00b2 = 9 + 16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D\u00b2 = 25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D = \u221a25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|D| = 5<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exemplo 5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Agora o vetor E:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/ddf8j-T-jabUNK2si7qXBlAJYZFiFzSHlpE0_SyF2Uu-u1L8VkBuox731tFY8cA-4aRIwK7PYoow3lGC3XyPLPkji_jWVeNiwNM2tVj_ioQYPFN0RgchH62gZ4fxM5ww1KH4R9wOyTpbUZH7UwoP-Q\" alt=\"\" width=\"270\" height=\"89\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ele possui dois componentes:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/ZF5ReQ4ECKwCN20fVJ0J2woG4YwQq4_XOo4GvllUa6IBPjdYsrNQ3hHTO24AmUhqtr8bn4VLwhOV4qTMNJeEbrzUHqDBUh-qLH_FJn50lHl_fIzmlh3rqdvO1tb5W2b71pN4KUCH6xbOGMP5WWFTbA\" alt=\"\" width=\"361\" height=\"121\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, sua f\u00f3rmula \u00e9:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/rbN_clvEkvSNPHUZlFwZTSAT97_JTbVia33c8dAYZXCeFJzOrSE33PCr6BsITYmwCix4j_D0Y0dy5UOGz6h6Gd3BhxfhkRK1_90437Te7dtORIgTwUaIbmzCCsqmCgxOXX_Ty6kjpCvpqErSxaD2mQ\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pit\u00e1goras nela!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E\u00b2 = 10i\u00b2 + 2j\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E\u00b2 = 10\u00b2 + 2\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E\u00b2 = 100 + 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E\u00b2 = 104<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">E = \u221a104<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|E| \u2245 10,2<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Exerc\u00edcios de versores<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Bom, agora que j\u00e1 entendemos o conceito de versores e como us\u00e1-los, vamos fazer alguns exerc\u00edcios para praticar:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Exerc\u00edcio 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Considere os tr\u00eas vetores a seguir<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/hkm2DDqA_3dEurNVxsLvl1eBvzprvQBatM8DMBr-agFfAe95Kdyw-0f0Txk5GfDPJ0VOb1cHZOdk2u1QHmmoBiUj2U9QkJ7f7WculreAQuhEgKwNA0dg2gxeW5VeQP9peI8_3P0xWpIsFlw18G6PzA\" alt=\"\" width=\"304\" height=\"166\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>a) Determine a intensidade do vetor soma:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/XYA50ha1Iz8YV_6HkLj8ehzAK1j_XDvCW3w-V76XBRzzfZjtlkLtE8MEx95dOHFAp8fRrOsXsJsMszupXUfb39UDgPNvnc1e_t0Wc_uTu8QysLhtKlD6mrSqUmfgUPiHYv5QZG_JYj-qRlC17v4BWg\" alt=\"\" width=\"174\" height=\"41\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Poder\u00edamos calcular o vetor resultante, mas vamos usar os versores. Ent\u00e3o:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/FmXiNh-xTuqk_DC7vSy7SA0PpLwGteEa3cUpM1AzMetRkk_mMKyoUK1-GHwu67iitrR11rDeNzxIN1EZ60sKLZ-Wr_RUKoeJPQSb784pACLS-LrTMNrHI3Gd5c6NRZfcnMcSq83N8Ih7deCB2ZEqbQ\" alt=\"\" width=\"102\" height=\"29\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/2ZzPCiN8jwKKFpOb7hOmimQRsEdbjOtspZgLmkljxjwZ_DH1qes0qZ3nr1dPuD1d2lG9krsPdhOYt_eDN2Vni4Cp2bhcZlt8JocLbEJNOPQp8jf3Fc9CR3mlA1NdjSr0wuyfKt11_5V4bdxQGydHAw\" alt=\"\" width=\"104\" height=\"27\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/S43c1BHLkVoxAnteglcJP2VDS1j7BAGujkiG1a0CDR30UBAk3FtXplt_kOkExJHp904SfAwNWnzIp6Qa4eiC7w94VlmpUgimUx55491kw67O_k_BDqGsUbWbiNw9R4tQulGKHzJZ8h4L32p7N8XuBQ\" alt=\"\" width=\"106\" height=\"29\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Agora \u00e9 s\u00f3 somarmos tudo:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/FNuFcs04S2hmjgCVGOP_EvYVmCAe9D9ut-9Xy1VEspdkrxo1JD3QoQdY14e0kM8kNTOzfRb8EzqGa6S4C6tLqcFzVJnFAThKPnKubNw4fnmbrBLJAQI3P4zDfaDnlZoRbeqeDVskPDCvFxk7fFBj5w\" alt=\"\" width=\"289\" height=\"24\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/z4Kyr6k7xkT7tbVDhGRB-ou89vtgQvizFiEJXPHySvtgiqSEZHA9cqeVeAUSv_6fVodOB16e6uec5xftlQ3eQpEaB2SZ0GIEppzFlhZcnLR9etPEVIyfs9vFOw12cPQzaLr2pXBofV2oWRZglGTVPg\" alt=\"\" width=\"87\" height=\"24\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se temos um vetor S que possui componente horizontal e vertical iguais, ent\u00e3o ele forma um \u00e2ngulo de 45\u00ba:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/Ih-Dc-G1KZYjvVvBKg2Ert6VLCUAFu8eRVDIlpRPpAVMal7RddAfGmFUsmmmSdxl6UYLH9egnOcUBg8Co83mf13kh8yelABnOujCMa1aDKhhFqCHSnoRsnMt74NWxrWFhR4YNyJE1736WVF2LKWh7A\" alt=\"\" width=\"127\" height=\"105\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ent\u00e3o, Pit\u00e1goras de novo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">S\u00b2 = 4\u00b2 + 4\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">S\u00b2 = 16 + 16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">S\u00b2 = 32<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">S = \u221a32<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Depois de aplicarmos a fatora\u00e7\u00e3o, temos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|S| = 4\u221a2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>b) Determine a intensidade do vetor&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/4fEhNYB3K6gaG0W9v8qD8jR_eRI4i1PPrQhKawJZWcuYLNE96Q1mMvPloiP9MNPEqM_QfFEDC6GqlNQdy3pKu177_1Wj4uFU7P17LYn3cc5fZzWeyfxMYgY6kV7TUFAvYyuAEcMFGkIdR5vkLhV9pA\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Primeiramente, vamos substituir os vetores da equa\u00e7\u00e3o pelas equa\u00e7\u00f5es que criamos acima:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/3YumrJncBbp0riY1Q5HPv-P_ibY9mEN7TiuXrXP--L04aG4ETQJUtzIXih0iafGZN834UI_tX5UE1m0Czh52ST3qGwnq-6CBPbakhFZ5th17Nv4kFi-q1YcBSQF35Z5cG1t9rf-AtNAcWniAnTv6Vg\" alt=\"\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/I13H3HjsvVggde_ZE1G-sbKbN7wglCVwItwcRl5iGAH-SU9O39tlQWpcZB_-z6M6iAwLtOMBofGIQf04PFfaeR660pw9WAPuGMllXxaKn5Am4L9TB9J_HhIIZQ--oPrsalZHC8b5DPY8ZarzcZUvig\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Como o vetor tem componentes horizontal e vertical, sabemos que forma um tri\u00e2ngulo ret\u00e2ngulo. Ent\u00e3o, \u00e9 s\u00f3 aplicar Pit\u00e1goras:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R\u00b2 = (-31)\u00b2 + (-20)\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R\u00b2 = 961 + 400<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R\u00b2 = 1361<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">R = \u221a1361<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">|R| \u2245 37<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#8211;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>SAIBA MAIS<\/strong><br>\ud83d\udc49\u00a0<a rel=\"noreferrer noopener\" href=\"https:\/\/professorpinguim.com.br\/blog\/decomposicao-de-um-vetor-em-dois-eixos\/\" target=\"_blank\"><strong>Proje\u00e7\u00e3o de um vetor em dois eixos<\/strong><\/a><br>\ud83d\udc49\u00a0<a rel=\"noreferrer noopener\" href=\"https:\/\/professorpinguim.com.br\/blog\/como-estudar-eletricidade-para-vestibulares-paulistas\/\" target=\"_blank\"><strong>Como estudar Eletricidade para vestibulares paulista<\/strong><\/a><br>\ud83d\udc49\u00a0<a rel=\"noreferrer noopener\" href=\"https:\/\/professorpinguim.com.br\/blog\/tudo-sobre-a-terceira-lei-de-newton\/\" target=\"_blank\"><strong>Tudo sobre a Terceira Lei de Newton<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vamos falar sobre versores: vamos rever os conceitos, repassar exemplos e resolver alguns exerc\u00edcios para memorizarmos a mat\u00e9ria.<\/p>\n","protected":false},"author":1,"featured_media":2672,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[729],"tags":[363,390,564,563,560,562,561,518],"class_list":["post-2669","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-eletrostatica","tag-cinematica","tag-cinematica-enem","tag-conceitos-versores","tag-exercicios-versores","tag-fisica-basica","tag-versores","tag-vetor","tag-vetores"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - 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