{"id":308254,"date":"2022-11-16T10:31:00","date_gmt":"2022-11-16T03:31:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=308254"},"modified":"2023-02-06T10:22:14","modified_gmt":"2023-02-06T03:22:14","slug":"contoh-soal-vektor-matematika","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/contoh-soal-vektor-matematika\/","title":{"rendered":"Contoh Soal Vektor Lengkap dengan Pembahasan"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

Hai Quipperian, saat belajar Fisika, tentu kamu sudah dikenalkan dengan besaran vektor kan? Apakah kamu masih ingat? Vektor adalah besaran yang memiliki besar dan arah. Ternyata, vektor juga dipelajari di Matematika, lho<\/em>. Bedanya, di Matematika kamu akan diarahkan lebih mendalam tentang kedudukan si vektor itu sendiri. Penasaran? Yuk, simak selengkapnya!<\/p>\n\n\n\n

Apa itu Vektor dan Apa Saja yang Dipelajari?<\/strong><\/h2>\n\n\n\n

Vektor adalah besaran yang memiliki besar\/nilai dan arah. Untuk menyatakan suatu vektor, kamu harus menyertakan tanda panah di atas lambang besarannya. Di artikel sebelumnya<\/a>, Quipper Blog sudah mengupas tuntas tentang Matematika Vektor ini. Di dalamnya membahas tentang sifat-sifat vektor, operasi vektor, notasi vektor, sampai penentuan koordinat.<\/p>\n\n\n\n

Di artikel ini, Quipper Blog akan mengulas beberapa contoh soal terkait vektor. Ayo belajar bersama-sama!<\/p>\n\n\n\n

Contoh Soal Vektor<\/strong><\/h2>\n\n\n\n

Contoh soal yang akan dibahas kali ini meliputi contoh soal vektor posisi, contoh soal vektor satuan, contoh soal panjang vektor, contoh soal perkalian vektor, contoh soal pengurangan vektor, dan contoh soal penjumlahan vektor.<\/p>\n\n\n\n

Contoh soal 1<\/strong><\/h3>\n\n\n\n

Diketahui besaran vektor seperti berikut.<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

Jika vektor posisi titik B adalah <\/sub>, vektor posisi titik A adalah \u2026.<\/p>\n\n\n\n

    \n
  1. <\/sub><\/li>\n\n\n\n
  2. <\/sub><\/li>\n\n\n\n
  3. <\/sub><\/li>\n\n\n\n
  4. <\/sub><\/li>\n\n\n\n
  5. <\/sub><\/li>\n<\/ol>\n\n\n\n

    Pembahasan:<\/p>\n\n\n\n

    Ingat, komponen vektor , merupakan hasil pengurangan antara vektor posisi titik B dan titik A, sehingga diperoleh:<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

     Jadi, vektor posisi titik A adalah <\/sub>.<\/p>\n\n\n\n

    Jawaban: A<\/p>\n\n\n\n

    Contoh soal 2<\/strong><\/h3>\n\n\n\n

    Diketahui dua buah vektor posisi seperti berikut.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Vektor <\/sub> bisa dinyatakan sebagai \u2026.<\/p>\n\n\n\n

      \n
    1. <\/sub><\/li>\n\n\n\n
    2. <\/sub><\/li>\n\n\n\n
    3. <\/sub><\/li>\n\n\n\n
    4. <\/sub><\/li>\n\n\n\n
    5. <\/sub><\/li>\n<\/ol>\n\n\n\n

      Pembahasan:<\/p>\n\n\n\n

       Vaktor <\/sub> merupakan hasil pengurangan antara vektor posisi di titik P dan vektor posisi di titik Q. Dengan demikian:<\/p>\n\n\n\n

      \"\"<\/figure>\n\n\n\n

      Jadi, vektor <\/sub> bisa dinyatakan sebagai <\/sub>.<\/p>\n\n\n\n

      Jawaban: B<\/p>\n\n\n\n

      Contoh soal 3<\/strong><\/h3>\n\n\n\n

      Diketahui koordinat titik K(2, -1, 3) dan titik L(1, 2, 1). Vektor satuan berikut yang searah dengan vektor KL adalah \u2026.<\/p>\n\n\n\n

        \n
      1. <\/sub><\/li>\n\n\n\n
      2. <\/sub><\/li>\n\n\n\n
      3. <\/sub><\/li>\n\n\n\n
      4. <\/sub><\/li>\n\n\n\n
      5. <\/sub><\/li>\n<\/ol>\n\n\n\n

        Pembahasan:<\/p>\n\n\n\n

        Mula-mula, kamu harus mencari dahulu vektor KL.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        Selanjutnya, tentukan vektor satuan yang searah dengan vektor KL.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        Jadi, vektor satuan yang searah dengan vektor KL adalah <\/sub>.<\/p>\n\n\n\n

        Jawaban: C<\/p>\n\n\n\n

        Contoh soal 4<\/strong><\/h3>\n\n\n\n

        Perhatikan titik koordinat Cartesius berikut.<\/p>\n\n\n\n

        \"\"<\/figure>\n\n\n\n

        Vektor satuan dari vektor A adalah \u2026.<\/p>\n\n\n\n

          \n
        1. <\/sub><\/li>\n\n\n\n
        2. <\/sub><\/li>\n\n\n\n
        3. <\/sub><\/li>\n\n\n\n
        4. <\/sub><\/li>\n\n\n\n
        5. <\/sub><\/li>\n<\/ol>\n\n\n\n

          Pembahasan:<\/p>\n\n\n\n

          Mula-mula, tentukan titik koordinat vektor A terlebih dahulu.<\/p>\n\n\n\n

          \"\"<\/figure>\n\n\n\n

          Lalu, tentukan vektor satuannya dengan persamaan berikut.<\/p>\n\n\n\n

          \"\"<\/figure>\n\n\n\n

          Jadi, vektor satuan dari vektor A adalah <\/sub>.<\/p>\n\n\n\n

          Jawaban: D<\/p>\n\n\n\n

          Contoh soal 5<\/strong><\/h3>\n\n\n\n

          Diketahui dua vektor posisi seperti berikut.<\/p>\n\n\n\n

          \"\"<\/figure>\n\n\n\n

          Jika panjang vektor  ST=10, nilai 2x<\/em> adalah \u2026.<\/p>\n\n\n\n

            \n
          1. 4<\/li>\n\n\n\n
          2. -8<\/li>\n\n\n\n
          3. 3<\/li>\n\n\n\n
          4. 5<\/li>\n\n\n\n
          5. -6<\/li>\n<\/ol>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Mula-mula, kamu harus menentukan vektor ST seperti berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Selanjutnya, gunakan persamaan panjang vektor untuk mencari nilai x<\/em>.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, nilai 2x<\/em> = 8 atau 2x<\/em> = 4.<\/p>\n\n\n\n

            Jawaban: A<\/p>\n\n\n\n

            Contoh soal 6<\/strong><\/h3>\n\n\n\n

            Perhatikan empat vektor berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Diketahui <\/sub>, berapakah nilai 2x<\/em> + 3y<\/em>  – z<\/em>?<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Diketahui perkalian titik <\/sub>. Untuk menyelesaikannya, kamu harus mengalikan elemen-elemen yang letaknya sama seperti berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Dengan demikian, diperoleh nilai x<\/em>, y<\/em>, dan z<\/em> berturut-turut adalah 2, -2, dan 6.<\/p>\n\n\n\n

            Jadi, nilai 2x<\/em> + 3y<\/em>  – z<\/em> = 2(2) + 3(-2) \u2013 6 = -8.<\/p>\n\n\n\n

            Contoh soal 7<\/strong><\/h3>\n\n\n\n

            Diketahui <\/sub> dan <\/sub> . Jika <\/sub>, berapakah hasil dari <\/sub>?<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Mula-mula, kamu harus menentukan hasil perkalian silang antara g dan h.<\/p>\n\n\n\n

            \"\"\/<\/figure>\n\n\n\n

            Selanjutnya, tentukan perkalian titik antara <\/sub> dan s.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, hasil dari <\/sub>adalah <\/sub>.<\/p>\n\n\n\n

            Contoh soal 8<\/strong><\/h3>\n\n\n\n

            Diketahui dua buah vektor berikut!<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jika hasil penjumlahan kedua vektor tersebut menghasilkan <\/sub>, tentukan nilai x<\/em> + y<\/em>!<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Penjumlahan dilakukan antara elemen yang seletak seperti berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, nilai x<\/em> + y<\/em> = 5 + 1 = 6.<\/p>\n\n\n\n

            Contoh soal 9<\/strong><\/h3>\n\n\n\n

            Jika <\/sub> dan <\/sub>, berapakah nilai <\/sub>?<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Mula-mula, kamu harus menentukan nilai pengurangan antara vektor p dan vektor q.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Lalu, tentukan nilai <\/sub> dengan cara berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, nilai <\/sub>.<\/p>\n\n\n\n

            Contoh soal 10<\/strong><\/h3>\n\n\n\n

            Perhatikan grafik berikut.<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jika <\/sub>dan <\/sub>, tentukan hasil dari <\/sub>!<\/p>\n\n\n\n

            Pembahasan:<\/p>\n\n\n\n

            Di soal ditanyakan hasil perkalian titik (skalar) antara dua vektor. Syarat perkalian itu adalah pangkal kedua vektor harus berimit di satu titik yang sama. Untuk memenuhi syarat itu, kamu bisa menggeser vektor w ke arah sumbu z positif seperti berikut.<\/p>\n\n\n\n

            \"\"\/<\/figure>\n\n\n\n

            Dengan demikian, diperoleh:<\/p>\n\n\n\n

            \"\"<\/figure>\n\n\n\n

            Jadi, hasil dari <\/sub>adalah 24.<\/p>\n\n\n\n

            Itulah pembahasan Quipper Blog kali ini. Semoga bisa kamu jadikan referensi belajar, ya. Jika ingin mendapatkan latihan soal lainnya, yuk buruan gabung Quipper Video. Bersama Quipper Video, belajar jadi lebih mudah dan menyenangkan. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"

            Hai Quipperian, saat belajar Fisika, tentu kamu sudah dikenalkan dengan besaran vektor kan? Apakah kamu masih ingat? Vektor adalah besaran yang memiliki besar dan…<\/p>\n","protected":false},"author":156447303,"featured_media":308259,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_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":[679384865],"tags":[679386732],"ppma_author":[679386823,679386836],"class_list":["post-308254","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika","tag-matematika-peminatan-kelas-10"],"acf":[],"yoast_head":"\nContoh Soal Vektor Lengkap dengan Pembahasan - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Memahami materi Vektor Matematika akan lebih cepat dengan mengerjakan contoh soal ini, dan lakukan evaluasi melalui penjelasannya. 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