Sumber : www.canva.com
A. DEFINISI
Menyatakan nilai dan arah dari suatu besaran. Vektor digambarkan sebagai anak panah. Anak panah menunjukkan arah yang ditunjuk vektor, sedangkan panjang anak panah menunjukkan besar kecilnya nilai vektor tersebut.
Menyatakan jumlah dari dua vektor atau lebih. Resultan vektor dapat dicari dengan menghubungkan pangkal vektor dengan ujung vektor. Metode-metode dalam menentukan resultan vektor antara lain :
- Metode segitiga : pada metode ini resultan diperoleh dengan menghubungkan pangkal vektor pertama dengan ujung vektor kedua
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjb1xcWBhwBn4dTqy6VbXVo9P9d8nOII5kDyRMYiwFmNCRyQVaIc24pjyxwx8jM3rAcGnJsAP5mgANHLp1-fT51WmTPIwnk8ZlKB8tL7zM_e4BnnxUeMohZFXDE_BQ84vy9dq1esTZQC8i2/w167-h120/image.png)
- Metode jajar genjang : menghubungkan diagonal dari kedua vektor
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhUN36FumLSsBfVep6NRNq_LlSWk6x9Sxet1OGR29eqLT48t8Gmqlsp-mvvBHrBEumkb6QodPzlT8iIi7r-_lFs9rGgjxMQU1CCGcxuv4Gt-Y0ZxGdL0_1xpdu2uuMn01ZkZJ6176BO-3B/w186-h94/image.png)
- Metode poligon : ujung vektor pertama dihubungkan dengan vektor selanjutnya.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiVaRFaC5vPgrebUiHHgS5lRD75ILk4w2qxG23V_75q59xvsx5uZuhWSjDUmSrtSM5KvPVBna_ogV-xqYSPALRyhWRgy0J709xU34xsWSIBaftH0-j3TI-qfFmrN6idnKk1bu7i_B1wYZwf/w155-h138/image.png)
C. SELISIH VEKTOR
Menyatakan pengurangan dua vektor atau lebih. Dapat menggunakan operasi hitung :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLiqwP70pHmRSe-nO9BXnIu-QS0r6U_ZO9phf5w21B5nXvCW1fsM5Wx0OU7yl1tNUR6EjwxRZ9LVF_bI7c60Q6Um1L3pqTamxvqxtUTM1et2gElObAl8EJVqZCBIA4r8qD0MSGR3_rajQi/w185-h104/image.png)
Contoh
Diketahui vektor A, B, dan C sebagai berikut :![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLiqwP70pHmRSe-nO9BXnIu-QS0r6U_ZO9phf5w21B5nXvCW1fsM5Wx0OU7yl1tNUR6EjwxRZ9LVF_bI7c60Q6Um1L3pqTamxvqxtUTM1et2gElObAl8EJVqZCBIA4r8qD0MSGR3_rajQi/w185-h104/image.png)
Tentukan :
(a) Resultan vektor (A+B)
(b) Selisih vektor (A – C)
jawab :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjne0nS5ttTgs2YxRNfxFVCguPqM9jopIHfjFzk9CgOSF_5ju9cYrtD-8afxdivEcfefvWiBpEBvaaMnDLFpFhGn_O0Nc3Lo9tOhb4lSCrU_s9eXPbPGhYS_cK3L5_uyQklxt56b4ZfJLHE/w134-h98/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdaNnEK-cRag7EIallnp67_rLNaOQg1McU6zd1bKD0iFvSuBKJ27Jb0PJTPFib2EtkL89HFF4lP4AWMMz6S5FHg73EhAJhybXYfCbqEBWAoM7z23axOYvI30py-JmncG1yX2xHOnexMUuB/w149-h102/image.png)
Nilai sebuah vektor memenuhi persamaan berikut :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXOAAJakGRAd48CQgvuYEuMUFMfsf5pbpXAKSFl_boK25Gmne3GcjwOaaKhXBt17HT9SyV0wWCiBNTC5jNeBfPIDRbMkEqFmmEnfEbE96JounnMSO3fPamtlE_FmG0fCqHChLZOGSE-Nys/w171-h64/image.png)
D. TRIGONOMETRI SEDERHANA
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzTpjTgY4W1GHOPm8RxplbRdebEKulYHK4kgq7uw_dzbQY33mOluUQMBMCTtu9v4hiGM9N0-X7lO22tzaavA16JRAFhbCpQdcw2zzhSzMXMrdsqdZd4h5flXLw2w2sSvJW8F4FCrxg3i2A/w320-h212/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuAtSRZ4ZTz_x3frZ9LcC1fR6UNCaAULsYGmvK0LImsb_usU6N7ZIFD9gV8Tkd3-yXmgPOglP4qvG-o-bGQ8JozCTtDlIODarne4fIuMUJJJJjH2_xDRVrW09P4MFAbEFGL3tfhlI8FLI7/w232-h133/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_m47X_fkBgsC517US7gFNbeM13QoMK6dVEGmpuC3KUFc0j0pHlZpU6LHwzgHbXC9kItKjqmmpxU-H-9RLmi8ZpTg00oZV2nc3birxDesvMt3O5PHT-Y9Kl4eFsaaOhiCvzIBk71c7WNH1/w218-h149/image.png)
E. RESULTAN VEKTOR METODE ANALITIK
(a) Resultan vektor (A+B)
(b) Selisih vektor (A – C)
jawab :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjne0nS5ttTgs2YxRNfxFVCguPqM9jopIHfjFzk9CgOSF_5ju9cYrtD-8afxdivEcfefvWiBpEBvaaMnDLFpFhGn_O0Nc3Lo9tOhb4lSCrU_s9eXPbPGhYS_cK3L5_uyQklxt56b4ZfJLHE/w134-h98/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdaNnEK-cRag7EIallnp67_rLNaOQg1McU6zd1bKD0iFvSuBKJ27Jb0PJTPFib2EtkL89HFF4lP4AWMMz6S5FHg73EhAJhybXYfCbqEBWAoM7z23axOYvI30py-JmncG1yX2xHOnexMUuB/w149-h102/image.png)
Nilai sebuah vektor memenuhi persamaan berikut :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXOAAJakGRAd48CQgvuYEuMUFMfsf5pbpXAKSFl_boK25Gmne3GcjwOaaKhXBt17HT9SyV0wWCiBNTC5jNeBfPIDRbMkEqFmmEnfEbE96JounnMSO3fPamtlE_FmG0fCqHChLZOGSE-Nys/w171-h64/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzTpjTgY4W1GHOPm8RxplbRdebEKulYHK4kgq7uw_dzbQY33mOluUQMBMCTtu9v4hiGM9N0-X7lO22tzaavA16JRAFhbCpQdcw2zzhSzMXMrdsqdZd4h5flXLw2w2sSvJW8F4FCrxg3i2A/w320-h212/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhuAtSRZ4ZTz_x3frZ9LcC1fR6UNCaAULsYGmvK0LImsb_usU6N7ZIFD9gV8Tkd3-yXmgPOglP4qvG-o-bGQ8JozCTtDlIODarne4fIuMUJJJJjH2_xDRVrW09P4MFAbEFGL3tfhlI8FLI7/w232-h133/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg_m47X_fkBgsC517US7gFNbeM13QoMK6dVEGmpuC3KUFc0j0pHlZpU6LHwzgHbXC9kItKjqmmpxU-H-9RLmi8ZpTg00oZV2nc3birxDesvMt3O5PHT-Y9Kl4eFsaaOhiCvzIBk71c7WNH1/w218-h149/image.png)
E. RESULTAN VEKTOR METODE ANALITIK
Vektor diuraikan menjadi komponen vektornya terhadap sumbu x dan terhadap sumbu y.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9JYQh7KxtwfO8gBOCEvbsxTSZwM0CV00URxEhyy5qeurcFbcmT4HN3zK3llkuAlYspm2fDGClK2LDLT2ZafGUS8eT7UlKZsJjoppLtezOjSJVpeyQXHH65rxdAemXLDGgHJGqH6vbIUfY/w136-h185/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZIKMc5xCztvSHcCnBcZRf5exaC6AGs_nfSYu96m4i7ZWXi8qDAAmBveH1TxAUJ_9Ndel6E01_ZdUmTgl3KZkIrRxGFNjAOkOc_yhFUzvg2tr64yig31j_lYrdzF1Gq7BJphYFuiu267ZC/w195-h143/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9JYQh7KxtwfO8gBOCEvbsxTSZwM0CV00URxEhyy5qeurcFbcmT4HN3zK3llkuAlYspm2fDGClK2LDLT2ZafGUS8eT7UlKZsJjoppLtezOjSJVpeyQXHH65rxdAemXLDGgHJGqH6vbIUfY/w136-h185/image.png)
contoh soal :
Tentukan komponen-komponen vektor pada sumbu-x dan sumbu-y dari vektor-vektor berikut :
a. Vektor A = 20 m pada arah 370
b. Vektor B =30 m pada arah 600
Tentukan komponen-komponen vektor pada sumbu-x dan sumbu-y dari vektor-vektor berikut :
a. Vektor A = 20 m pada arah 370
b. Vektor B =30 m pada arah 600
jawab :
(a)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsLXiY1dynMj0HZ_Oz7OZRfz73AusyGWpbfKp7U9Dg6pNJOrMGT6ggNXRoNunNi9rtSTM9WVVZm9E3TUJqh5BI2S_TaQEMQuSh1smJMTP5-YTntTNOwF1jgCSxehuqPkIqUuvaj-NO5vPh/w223-h153/image.png)
(b)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGp40opD8o8PdPSkhROCMRHzCugYxsRWLEajGpw7ppcUUoAVejNZMSPiWGqXAaec2JONB5vn7w9qizeMn6RnQUMCsLcMJav8oGF1Wi_aLGhzHON1sw0M45MOBUrgxSjCb2FfMMudBVI2LX/w251-h170/image.png)
F. RESULTAN VEKTOR ATURAN COSINUS
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgsLXiY1dynMj0HZ_Oz7OZRfz73AusyGWpbfKp7U9Dg6pNJOrMGT6ggNXRoNunNi9rtSTM9WVVZm9E3TUJqh5BI2S_TaQEMQuSh1smJMTP5-YTntTNOwF1jgCSxehuqPkIqUuvaj-NO5vPh/w223-h153/image.png)
(b)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgGp40opD8o8PdPSkhROCMRHzCugYxsRWLEajGpw7ppcUUoAVejNZMSPiWGqXAaec2JONB5vn7w9qizeMn6RnQUMCsLcMJav8oGF1Wi_aLGhzHON1sw0M45MOBUrgxSjCb2FfMMudBVI2LX/w251-h170/image.png)
F. RESULTAN VEKTOR ATURAN COSINUS
Jika sudut antara kedua vektor ≠ 90⁰ tapi lebih kecil dari 180⁰ . Resultan dua vektor dapat ditentukan dengan aturan cosinus :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEib7fny4ItSl98quGaYvM21CtDrudX4ouWp9TVJdVkHPXGUP_JP1j9TDmG8rbnSV_s8YqBOCxogz1UWpGbt-NkGhVHIy-RGTi4cHOxi2zmBQetvgVzOfDKZhlIm8RvZ7-ryCmlKI3S26TIo/w251-h30/image.png)
arah resultan :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5StKR0f_F_7etvzbXauvnma1iqZ8Z0KcYEz4o00eudvPoSqL7cUdhPHfDQL4bbtmEZC-pciCKj_C6d-OMayUzlF5qJAFKN46DAi9UqbrrCjYl5kzjZPKmcgDVBv8XYMFVW7v9S9KoPCnf/w169-h47/image.png)
contoh soal :
Perhatikan gambar di bawah ini ! Tentukan resultan ketiga vektor gaya tersebut ?
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik2AGzEWqdu3im_YWw3A2tK-bpAxlPbaVX0FYFz8BaKThqHNN0zu7wlcIFxaqgJ8mYnx3wdPv2Gumduibzwu43Lvhtd7TjPf8hCLi0NwWkY8p71IR2-212-S4JN0fZhaTSeNCeIuAW11Uu/w252-h202/image.png)
Perhatikan gambar di bawah ini ! Tentukan resultan ketiga vektor gaya tersebut ?
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEik2AGzEWqdu3im_YWw3A2tK-bpAxlPbaVX0FYFz8BaKThqHNN0zu7wlcIFxaqgJ8mYnx3wdPv2Gumduibzwu43Lvhtd7TjPf8hCLi0NwWkY8p71IR2-212-S4JN0fZhaTSeNCeIuAW11Uu/w252-h202/image.png)
jawab :
Uraikan setiap vektor gaya terhadap sumbu x dan sumbu y
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiurX-w4buSPGKa_lQZfDQV7fyyaRs9P1tFIIA8uD5Qk9VomSC-246j8-YWZykFY31IXRZFzR42Qzmd_COE42LmAoPjWG43hWeJjtC7NGrQxF-8v-bCVbjGnBYaRq1FHv98tE9jTmZCQ2ad/w261-h203/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiP_bCUlAgSbIgrjD6E4n8AcyqnYOznxFxPdoRL9VYEiYSy1oTL527cMgkh8YokoHuNZPMmZMU6atlLQmuirs3JonoVgrPg6fjjQEs_5NgeFHazZJfpdgor-CcD5y_TIavhUPZ2NiDFpANc/w275-h160/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCk47_I3ODceUyw4NN8Bw4dD14IsUHmARlZ1TIGtRSDaMw7np7KpOzCIIsKAhqRAoVrfoqghtep1ei6V8ec0Xr_vKirIhYU4GhyphenhyphenVz_xatOl0ykHXF0kDC4-OGi8baIxTRJm_BRTczTA9hu/w205-h269/image.png)
G. PERKALIAN VEKTOR
terbagi dua :
- Perkalian titik /dot. Menghasilkan besaran skalar
Perkalian skalar dengan vektor satuan ā = (x1, y1, z1 ) dengan ḃ = (x2, y2, z2 ) dapat dihitung dengan persamaan :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgyYuKVNE-bvM3zrfzG3dYCh1VMV16N35pjJztxEfen7n1zKJv12we9GEjEb4mTQH9AooImmalU3nFcAq3b4m34mRrbrFQpMDdD32oh8LPa69_HAixVAc2nk2L5s4BIwE9sDxYHbE6PLJ8m/w282-h31/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhahJJjuGgKINGbUuWYBSBAIZVp6VHy51UUBIwsNJxRNcQkSJO0TGDpfvRYczbhS-3G6ifO3-vQohWUtXmqvHlUOWWWuG6nf1eP80XDZeeLgduav_XoVF9_U9fn5FzBiqUv3BxhVJQjRWCF/w112-h47/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqOiOFIL_7D-IQUUPHOnMQtw9XhDScomaDyHGYH-12XQaPEVfh1itdxnyQZzWJWM_PGSsuJzu4T3Ii3BwUcCMovBxkrhIUyq6f8p_YHSvbMP1Ghd_uqB0QZlrOHYBHh22iHyU-MdqNQcDn/w162-h39/image.png)
- Perkalian silang /cross
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhS0-S1ZKTe63uOuqk_2h_OPzj3k5rmUFfOiCkAF_jmlI5OMWSg4jB2HB9jlf7Vus7K7Tjqb4Zggn1JeGtW4Y1RK6C2oLPTx9PsrrVrAxB6mRkrEKw-JNYuJtnZ-ucfoCPGgUtY6JQHUE8s/w209-h29/image.png)
contoh :
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgtXkh8FoKJ-wg1X42VsOJvphuVqBXdEIF09EmNrDRen7hf0IFjr_M6WGqEGQGd130xjl7_WGG3NbaFlObOKb9Fm6X8NawXAMCGawQpwZRDGk00WES8HJbcbNFH0Wdv6aCHuYEHHiI49AU6/w144-h103/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjC2a4Dl-btngMNqk99N9AfNXEXAR6ZKHzEtXXSagxrFyx78kgq_pEFPmcy4lRgEYnpfFUyZbFGgFUqNhj7FqGBIsF7E0I6y1IFes2R8Nf9SuYbXXJSOmNxXzEuuxLZNSX-J5xILC_L5NlI/w212-h56/image.png)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBarmCpzI4dqqJ1XBMeqaIUE0n9slqvYPlDNHy8Kdxt0Qt3hhQ8W8e5WXaYucF7I0pGJcylyBBIPZhvWRhdRv9PYO6A-PgojCJ0c3hO6YgwmAleB86MHt3GlxdZ56p-m97HOtKB1EK2dFt/w456-h30/image.png)
Oke adik-adik demikianlah penjelasan mengenai materi vektor. Vektor ini akan kalian pelajari di awal semester satu. Semoga bermanfaat dan bisa jadi referensi untuk belajar di rumah.. selamat belajar😊
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