{"id":6062,"date":"2022-01-19T09:00:00","date_gmt":"2022-01-19T12:00:00","guid":{"rendered":"https:\/\/professorpinguim.com.br\/blog\/?p=6062"},"modified":"2024-04-27T12:38:24","modified_gmt":"2024-04-27T15:38:24","slug":"exercicios-resolvidos-sobre-vetores","status":"publish","type":"post","link":"https:\/\/professorpinguim.com.br\/blog\/exercicios-resolvidos-sobre-vetores\/","title":{"rendered":"Exerc\u00edcios resolvidos sobre Vetores"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Exerc\u00edcios sobre Vetores<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Um autom\u00f3vel se desloca 6 km para norte e, em seguida, 8 km para o leste. Determine a intensidade do vetor deslocamento.<\/strong><\/p>\n\n\n\n<!--more-->\n\n\n\n<p class=\"wp-block-paragraph\">Vamos chamar o deslocamento para o norte de d1 e o deslocamento para o leste de d2. Veja:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"203\" height=\"167\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image.png\" alt=\"\" class=\"wp-image-30514\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pela regra do pol\u00edgono de soma vetorial, basta ligarmos os dois deslocamentos (in\u00edcio de um com o final de outro) para formarmos, neste caso, um tri\u00e2ngulo ret\u00e2ngulo. A este novo vetor daremos o nome de deslocamento total (dT). Observe:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"204\" height=\"171\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-1.png\" alt=\"\" class=\"wp-image-30516\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Importante: dT = d1 + d2. No entanto, n\u00e3o devemos substituir esses elementos por n\u00fameros. Como nesta quest\u00e3o a figura formada foi um tri\u00e2ngulo ret\u00e2ngulo, ent\u00e3o devemos utilizar Pit\u00e1goras:\u00c7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d<sub>T<\/sub>\u00b2 = 6\u00b2 + 8\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d<sub>T<\/sub> = 10 km<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Uma pessoa caminha em uma plan\u00edcie realizando tr\u00eas movimentos retil\u00edneos: primeiro percorre 10 km de sul para norte; em seguida, percorre 6 km de oeste para leste; finalmente, caminha mais dois quil\u00f4metros de norte para sul.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>a) Desenhe os vetores deslocamento de cada trecho, assim como o vetor deslocamento total, <\/strong><strong>d<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">De novo: o primeiro deslocamento, de 10 km para norte, chamaremos de d1 . O segundo, para leste, daremos o nome de d2 . Por fim, o \u00faltimo, para o sul, ser\u00e1 nosso d3. Veja:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-2.png\" alt=\"\" class=\"wp-image-30517\" width=\"164\" height=\"158\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para encontrar o deslocamento total pedido pela quest\u00e3o, mais uma vez devemos ligar o in\u00edcio do primeiro ao final do \u00faltimo trecho:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"202\" height=\"197\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-3.png\" alt=\"\" class=\"wp-image-30518\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>b) Calcule o m\u00f3dulo de <\/strong><strong>d<\/strong><strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Lembre-se de que o deslocamento final \u00e9 igual \u00e0 soma vetorial dos outros tr\u00eas deslocamentos: d = d1 + d2 + d3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Como n\u00e3o podemos colocar n\u00fameros nessa equa\u00e7\u00e3o de vetores, para calcular o m\u00f3dulo, podemos colocar na figura quanto vale cada lado da figura formada pelos deslocamentos:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"162\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-4.png\" alt=\"\" class=\"wp-image-30519\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Note que, para encontrarmos o deslocamento total, podemos formar um tri\u00e2ngulo em que o lado que queremos descobrir desempenha o papel da hipotenusa. Portanto, o deslocamento pedido pela quest\u00e3o, tem um cateto que vale 6 e outro que vale 8 (repare na figura: 10 &#8211; 2).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Novamente lan\u00e7ando m\u00e3o de Pit\u00e1goras, temos:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d\u00b2 = 6\u00b2 + 8\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d = 10 km<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>(PUCCAMP 98) Num bairro, onde todos os quarteir\u00f5es s\u00e3o quadrados e as ruas paralelas distam 100m uma da outra, um transeunte faz o percurso de P a Q pela trajet\u00f3ria representada no esquema a seguir.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"291\" height=\"228\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-5.png\" alt=\"\" class=\"wp-image-30520\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O deslocamento vetorial desse transeunte tem m\u00f3dulo, em metros, igual a<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>a) 300<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>b) 350<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>c) 400<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>d) 500<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>e) 700<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para calcularmos o deslocamento vetorial, temos que desenhar o vetor que parte do ponto P ao Q. Portanto:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"200\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-6.png\" alt=\"\" class=\"wp-image-30521\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Repare que, para calcular o m\u00f3dulo, novamente vamos utilizar a figura formada. Afinal, temos o valor dos catetos que ser\u00e3o formados:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"263\" height=\"170\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-7.png\" alt=\"\" class=\"wp-image-30522\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Assim: d\u00b2 = 300\u00b2 + 400\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d = 500 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">RESPOSTA: D<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 4<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Um p\u00e1ssaro voa em linha reta do ponto A, no solo, ao ponto B, em uma montanha, que dista 800 m do ponto A ao longo da horizontal. O ponto B se encontra tamb\u00e9m a uma altura de 600 m em rela\u00e7\u00e3o ao solo.Dado que a velocidade do p\u00e1ssaro \u00e9 de 10 m\/s, determine o intervalo de tempo que ele leva para percorrer a dist\u00e2ncia de A a B. (considere g = 10 m\/s<\/strong><strong><sup>2<\/sup><\/strong><strong>).&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Note que o ponto A est\u00e1 na horizontal e o ponto B est\u00e1 na vertical:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"382\" height=\"241\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-8.png\" alt=\"\" class=\"wp-image-30523\" srcset=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-8.png 382w, https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-8-300x189.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Voc\u00ea j\u00e1 deve ter percebido que o deslocamento entre A e B vai formar um tri\u00e2ngulo ret\u00e2ngulo. Portanto:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d\u00b2 = 600\u00b2 + 800\u00b2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d = 1000 m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Agora, como a quest\u00e3o pede o tempo, vamos usar a f\u00f3rmula da velocidade:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">v=\u0394s\/\u0394t<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"121\" height=\"59\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-9.png\" alt=\"\" class=\"wp-image-30524\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">\u0394t = 100 s<\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Desenhe o vetor :<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"138\" height=\"37\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-10.png\" alt=\"\" class=\"wp-image-30525\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-11.png\" alt=\"\" class=\"wp-image-30526\" width=\"566\" height=\"443\" srcset=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-11.png 603w, https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-11-300x235.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">a) Veja que, quando os vetores est\u00e3o desenhados com a mesma origem, podemos usar a regra do paralelogramo:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"206\" height=\"171\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-12.png\" alt=\"\" class=\"wp-image-30527\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">b) Quando temos um vetor saindo da origem de outro, devemos utilizar a regra do pol\u00edgono, unindo a origem de um com o final de outro:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"157\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-13.png\" alt=\"\" class=\"wp-image-30528\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">c) Novamente os vetores est\u00e3o com a mesma origem. Ent\u00e3o, vamos tra\u00e7ar as paralelas:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"262\" height=\"222\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-14.png\" alt=\"\" class=\"wp-image-30529\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">d) Mesma solu\u00e7\u00e3o:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"259\" height=\"274\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-15.png\" alt=\"\" class=\"wp-image-30530\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Quest\u00e3o 6<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>O vetor A a seguir tem m\u00f3dulo 40 unidades. Determine suas componentes horizontal e vertical.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"291\" height=\"276\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-16.png\" alt=\"\" class=\"wp-image-30531\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Nesta quest\u00e3o, devemos decompor os vetores. Para isso, devemos tra\u00e7ar em A uma paralela ao eixo y. Isso nos dar\u00e1 o vetor Ax.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"316\" height=\"288\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-17.png\" alt=\"\" class=\"wp-image-30532\" srcset=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-17.png 316w, https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-17-300x273.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Note que formaremos um tri\u00e2ngulo, do qual teremos que utilizar o cosseno do \u00e2ngulo de 60\u00ba:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-24.png\" alt=\"\" class=\"wp-image-30539\" width=\"147\" height=\"175\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para encontrar o outro componente, precisamos tra\u00e7ar em A uma paralela no eixo x, que nos dar\u00e1 Ay. Novamente, formaremos um tri\u00e2ngulo. E repara que, pela conforma\u00e7\u00e3o da figura, o \u00e2ngulo ser\u00e1 o mesmo, s\u00f3 que dessa vez ser\u00e1 o seno:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"333\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-18.png\" alt=\"\" class=\"wp-image-30533\" srcset=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-18.png 313w, https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-18-282x300.png 282w\" sizes=\"(max-width: 313px) 100vw, 313px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-20.png\" alt=\"\" class=\"wp-image-30535\" width=\"168\" height=\"180\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"292\" height=\"212\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-19.png\" alt=\"\" class=\"wp-image-30534\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Faremos a mesma coisa. Comecemos tra\u00e7ando uma paralela ao eixo y para encontramos o vetor Ax.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/C0LTW8c8spfin8XuKVKtIQj7TFKkZ8m9B0ux0JzJoE3htHVoWaZBMMoAsYpyGdl8UINybAv0aHLSnq6vCSoXw_C5zmf89ixONT5vRjt3WU4QXs-qWiof86IZLNw7Tfiopz5QUtVY\" alt=\"tra\u00e7ando uma paralela ao eixo y \"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-23.png\" alt=\"\" class=\"wp-image-30538\" width=\"181\" height=\"229\" srcset=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-23.png 239w, https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-23-237x300.png 237w\" sizes=\"(max-width: 181px) 100vw, 181px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Agora note que, quando o \u00e2ngulo \u00e9 45\u00ba, o vetor A corta um \u00e2ngulo de 90\u00ba exatamente na metade. Portanto, a componente Ay tem o mesmo tamanho que Ax: <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"210\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-22.png\" alt=\"\" class=\"wp-image-30537\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se voc\u00ea quiser fazer as contas mesmo assim:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-21.png\" alt=\"\" class=\"wp-image-30536\" width=\"163\" height=\"228\" srcset=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-21.png 219w, https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2024\/04\/image-21-215x300.png 215w\" sizes=\"(max-width: 163px) 100vw, 163px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Para aprender um pouco mais sobre vetores, assista minha videoaula abaixo:<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Aula 1<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-embed aligncenter is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"VETORES \ud83d\udd25 parte 1 | Destrave a F\u00edsica\ud83d\udc27 Professor Pinguim\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/TAqLyOxfJv0?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Aula 2<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-embed aligncenter is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"VETORES \ud83d\udd25 parte 2 | Destrave a F\u00edsica\ud83d\udc27 Professor Pinguim\" width=\"800\" height=\"450\" src=\"https:\/\/www.youtube.com\/embed\/FTxx9ZkFfok?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\">E se quiser ajuda para melhorar seu n\u00edvel de F\u00edsica em outras mat\u00e9rias,&nbsp;<a href=\"https:\/\/professorpinguim.com.br\/\"><strong>entre em contato comigo e escolha o curso de F\u00edsica mais adequado para voc\u00ea<\/strong><\/a><strong>!<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/conteudo.professorpinguim.com.br\/curso-de-fisica-gratuito\" target=\"_blank\" rel=\"https:\/\/pinguim.webflow.io\/extensivo-enem-vestibulares-sp\/extensivo-enem-vestibulares-sp noopener noreferrer\"><img decoding=\"async\" src=\"https:\/\/professorpinguim.com.br\/blog\/wp-content\/uploads\/2022\/05\/curso-fisica-professor-pinguim.png\" alt=\"Curso de F\u00edsica Gr\u00e1tis do Professor Pinguim\" class=\"wp-image-11364\"\/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>SAIBA MAIS<\/strong><br>\ud83d\udc49&nbsp;<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&nbsp;<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 <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\n\n\n<p class=\"wp-block-paragraph\">Me acompanhe nas redes sociais: curta a minha&nbsp;<a href=\"https:\/\/www.facebook.com\/professorpinguim\/\"><strong>p\u00e1gina no Facebook<\/strong><\/a><strong>,<\/strong>&nbsp;me&nbsp;siga no&nbsp;<a href=\"https:\/\/www.instagram.com\/professorpinguim\/\"><strong>Instagram<\/strong><\/a><strong>,<\/strong>&nbsp;se inscreva no&nbsp;<a href=\"https:\/\/www.youtube.com\/c\/PinguimV%C3%ADdeoF%C3%ADsica\/?sub_confirmation=1\"><strong>Youtube<\/strong><\/a>&nbsp;e participe do meu canal oficial no&nbsp;<strong><a href=\"https:\/\/professorpinguim.com.br\/telegram\">Telegram<\/a><\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Nesta aula, vamos resolver juntos alguns exerc\u00edcios sobre soma de vetores.<\/p>\n","protected":false},"author":1,"featured_media":6063,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[729],"tags":[728,711,712,561],"class_list":["post-6062","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-eletrostatica","tag-deslocamento-vetorial","tag-exercicios-sobre-soma-de-vetores","tag-exercicios-vetores","tag-vetor"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exerc\u00edcios resolvidos sobre Vetores - Professor Pinguim | F\u00edsica<\/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:\/\/professorpinguim.com.br\/blog\/exercicios-resolvidos-sobre-vetores\/\" \/>\n<meta property=\"og:locale\" content=\"pt_BR\" \/>\n<meta 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