{"id":70652,"date":"2017-03-22T14:49:13","date_gmt":"2017-03-22T07:49:13","guid":{"rendered":"https:\/\/video.quipper.com\/id\/blog\/?p=70652"},"modified":"2021-11-24T21:51:07","modified_gmt":"2021-11-24T14:51:07","slug":"mau-siap-menghadapi-un-matematika-ini-5-contoh-soal-vektor-matematika-sma-kelas-10","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/matematika-un-sma\/mau-siap-menghadapi-un-matematika-ini-5-contoh-soal-vektor-matematika-sma-kelas-10\/","title":{"rendered":"Mau Siap Menghadapi UN Matematika? Ini 5 Contoh Soal Vektor Matematika SMA Kelas 10!"},"content":{"rendered":"

\"Mau<\/a><\/p>\n

Quipperian, bagaimana persiapanmu untuk menghadapi Ujian Nasional (UN) 2017 pelajaran matematika? Masih bingung? Merasa belum siap? Tenang saja, ada Quipper Video Blog yang akan membantumu.<\/p>\n

Pada artikel kali ini, Quipper akan membahas tentang contoh soal bab vektor dalam pelajaran matematika. Dengan mempelajari beberapa contoh soal ini, semoga saja dapat membuatmu lebih percaya diri menghadapi UN Matematika 2017. Langsung saja, yuk, disimak!<\/span><\/p>\n

Soal 1<\/b><\/h2>\n

Jika a = i – 2j + k, b = 2i – 2j – 3k dan c = -i + j + 2k, maka 2a – 3b – 5 c sama dengan:<\/b><\/p>\n

A. i + j + k<\/span><\/p>\n

B. 2i – 5j + k<\/span><\/p>\n

C. 5i – 2j + k<\/span><\/p>\n

D. 5i + 2j + k<\/span><\/p>\n

E. i – 2 j \u2013 k<\/span><\/p>\n

Untuk menjawab soal itu, Quipperian harus memperhatikan pembahasannya berikut:<\/span><\/p>\n

2a – 3b – 5 c = 2 (i – 2j + k) -3(2i – 2j – 3k) – 5(-i + j + 2k)<\/span><\/p>\n

2a – 3b – 5c = 2i – 4j + 2k – 6i + 6j + 9k + 5i – 5j – 10k = i + j + k<\/span><\/p>\n

Dari hasil hitungan itu, maka jawaban yang tepat ialah <\/span>A<\/b>.<\/span><\/p>\n

Soal 2<\/b><\/h2>\n

Misalkan D adalah titik berat segitiga ABC dimana A(2,3,-2), B(-4,1,2) dan C(8,5,-3). Panjang vektor posisi d sama dengan:<\/b><\/p>\n

A. 3<\/span><\/p>\n

B. 5<\/span><\/p>\n

C. \u221a5<\/span><\/p>\n

D. \u221a14<\/span><\/p>\n

E. \u221a13<\/span><\/p>\n

Agar dapat menjawab soal ini, hal pertama yang harus kamu lakukan ialah mencari titik D terlebih dahulu. Titik D merupakan titik berat segitiga dalam soal tersebut. Maka, D= 1\/3 (A + B + C).<\/span><\/p>\n

Dari temuan rumus itu, kamu tinggal memasukkan nilai dari masing-masing titik A, B, dan C. Berikut cara menghitungnya:<\/span><\/p>\n

D = 1\/3 (2,3,-2) + (-4,1,2) + (8,5,-3)<\/span><\/p>\n

D = 1\/3 (6,9,-3) = (2,3,-1)<\/span><\/p>\n

Setelah menemukan titik D, hitungan yang harus kamu lakukan selanjutnya ialah panjang proyeksi titik D. <\/span><\/p>\n

Berikut cara penghitungannya:<\/span><\/p>\n

\"Mau<\/a><\/p>\n

Dari pilihan jawaban yang ada maka jawaban yang tepat untuk soal tersebut ialah <\/span>D<\/b>.<\/span><\/p>\n

Jangan Anggap Remeh Materi Ini di Ujian Nasional Matematika Besok!<\/a><\/h3>\n

Soal 3<\/b><\/h2>\n

Diketahui dua vektor u = 4i – mj + 2 k dan v = 5i + 2j – 4k saling tegak lurus. Maka harga m adalah:<\/b><\/p>\n

A. 10<\/span><\/p>\n

B. 6<\/span><\/p>\n

C. 5<\/span><\/p>\n

D. 9<\/span><\/p>\n

E. 1<\/span><\/p>\n

Merujuk pada soal tersebut, vektor u dan v saling tegak lurus maka rumusnya sama seperti: u.v = 0. Dengan begitu, untuk mencari harga m, maka rumus tersebutlah yang digunakan dengan memasukkan persamaan yang telah diketahui. Hitungannya menjadi seperti berikut:<\/span><\/p>\n

u . v = 0<\/span><\/p>\n

(4i – mj + 2k) (5i + 2j – 4k) = 20 – 2m – 8 = 0 <\/span><\/p>\n

m = 6<\/span><\/p>\n

Dari hasil hitungan tersebut maka pilihan jawaban yang tC. epat ialah <\/span>B<\/b>.<\/span><\/p>\n

Soal 4<\/b><\/h2>\n

Diketahui A (1,2,3), B(3,3,1) dan C(7,5,-3). Jika A, B, dan C segaris, perbandingan AB : BC =…<\/b><\/p>\n

A. 5 : 2<\/span><\/p>\n

B. 2 : 1<\/span><\/p>\n

C. 1 : 2<\/span><\/p>\n

D. 5 : 7<\/span><\/p>\n

E. 7 : 3<\/span><\/p>\n

Untuk menyelesaikan soal tersebut, maka hitungan rumusnya sebagai berikut:<\/span><\/p>\n

AB = B – A = (3,3,1) – (1,2,3) = (2,1,-2)<\/span><\/p>\n

Besar AB = \u221a22 + 12 + (-2)2 = 3 <\/span><\/p>\n

BC = C – B = (7,5,-3) – (3,3,1) = (4,2,-4)<\/span><\/p>\n

Besar BC = \u221a42 + 22 + (-4)2 = 6<\/span><\/p>\n

Dari hasil hitungan tersebut maka perbandingan AB : BC = 3 : 6 = 1 : 2. Dengan demikian, jawaban yang tepat untuk soal tersebut ialah pilihan <\/span>C<\/b>.<\/span><\/p>\n

Yuk Belajar Mencintai Matematika Agar Kamu Siap Menghadapi UN 2017!<\/a><\/h3>\n

Soal 5<\/b><\/h2>\n

Ditentukan A(4 , 7 , 0) , B(6 , 10 , \u20136) dan C(1 , 9 , 0). AB dan AC wakil-wakil dari vektor u dan v. Besar sudut antara u dan v adalah:<\/b><\/p>\n

A. \u03a0<\/span><\/p>\n

B. 0<\/span><\/p>\n

C. 1\/4 \u03c0<\/span><\/p>\n

D. 1\/2 \u03c0<\/span><\/p>\n

E. 3\/4 \u03c0<\/span><\/p>\n

Agar dapat menjawab soal tersebut, hal pertama yang harus Quipperian lakukan ialah tentukan vektor u dan v terlebih dahulu dengan rumus berikut:<\/span><\/p>\n

u = AB = B \u2212 A = (6 , 10 , \u20136) \u2212 (4 , 7 , 0) = (2, 3, \u22126) \u2192 u = 2i + 3j \u2212 6k<\/span><\/p>\n

v = AC = C \u2212 A = (1 , 9 , 0) \u2212 (4 , 7 , 0) = (\u2212 3, 2, 0) \u2192 v = \u2212 3i + 2j<\/span><\/p>\n

Setelah itu, barulah mencari besar sudut u dan v dengan menggunakan rumus berikut:<\/span><\/p>\n

cos<\/span> \u03b1= <\/span>u.v<\/span>|<\/span>u<\/span>||<\/span>v<\/span>|<\/span><\/p>\n

cos<\/span> \u03b1= <\/span>(<\/span>2i + 3j – 6k<\/span>)<\/span>(- 3i + 2j) <\/span>2<\/span>2<\/span>+ <\/span>3<\/span>2<\/span>+<\/span>(<\/span>– <\/span>6<\/span>2<\/span>)<\/span>(<\/span>-3<\/span>)<\/span>2<\/span>+<\/span>2<\/span>2<\/span>+<\/span>0<\/span>2<\/span><\/p>\n

cos<\/span> \u03b1= <\/span>-6+6+0<\/span>49<\/span> 12<\/span> = <\/span>0<\/span>7<\/span>12<\/span>=0<\/span><\/p>\n

Dari hasil hitungan tersebut, sudut dengan nilai cosinus nol adalah <\/span>90<\/span>0<\/span> atau sama dengan<\/span> 1\/2 \u03c0. Jadi, jawaban yang tepat untuk soal tersebut ialah <\/span>D<\/b>.<\/span><\/p>\n

Itulah lima contoh soal UN Matematika 2017 mengenai bab vektor. Bila kamu ingin melatih diri dan mempersiapkan diri dengan matang untuk menghadapi UN, maka kamu bisa berlatih bersama Quipper Video. Sebab, di dalamnya terdapat banyak contoh soal dan materi mengenai mata pelajaran matematika, khususnya bab vektor.<\/span><\/p>\n

Dengan persiapan yang matang, pastinya nilai sempurna bisa kamu raih. Tetap semangat ya Quipperian belajarnya!<\/span><\/p>\n

Penulis: Muhammad Khairil<\/b>
\n<\/b><\/p>\n","protected":false},"excerpt":{"rendered":"

Quipperian, bagaimana persiapanmu untuk menghadapi Ujian Nasional (UN) 2017 pelajaran matematika? Masih bingung? Merasa belum siap? Tenang saja, ada Quipper Video Blog yang akan…<\/p>\n","protected":false},"author":156446345,"featured_media":71482,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[677999210],"tags":[],"ppma_author":[679386822],"class_list":["post-70652","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika-un-sma"],"acf":[],"yoast_head":"\nMau Siap Menghadapi UN Matematika? 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