Iklan

Iklan

Pertanyaan

Diketahui vektor a = 5 i − 12 j ​ dan b = ( 3 , 4 ) , vektor c = − 2 i − 6 j ​ . Tentukan: a) vektor a − 2 b − c b) vektor 2 a + b − 2 1 ​ c

Diketahui vektor  dan , vektor . Tentukan:

a) vektor 

b) vektor 

Iklan

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

diperoleh dan .

diperoleh a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top equals i with hat on top plus 2 j with hat on top dan 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top equals 14 i with hat on top minus 25 j with hat on top.

Iklan

Pembahasan

Ingat kemabli konsep operasi hitung vektor. Untuk a dan b vektor-vektor pada dua dimensi, berlaku: a ± b ​ = = ​ ( a 1 ​ , a 2 ​ ) + ( b 1 ​ , b 2 ​ ) ( a 1 ​ + b 1 ​ , a 2 ​ + b 2 ​ ) ​ Perkalian skalar dengan vektor. Jika k skalar tak nol dan vektor a = ( a 1 ​ , a 2 ​ , ... a n ​ ) , maka k a = ( k a 1 ​ , k a 2 ​ , ... k a n ​ ) . Diketahui: vektor dan , vektor . a) menentukan vektor b) menentukan vektor Jadi, diperoleh dan .

Ingat kemabli konsep operasi hitung vektor.

Untuk a dan b vektor-vektor pada dua dimensi, berlaku:

Perkalian skalar dengan vektor.

Jika  skalar tak nol dan vektor , maka .

Diketahui:

vektor a with rightwards arrow on top equals 5 i with hat on top minus 12 j with hat on top dan b with rightwards arrow on top equals left parenthesis 3 comma space 4 right parenthesis equals 3 i with hat on top plus 4 j with hat on top, vektor c with rightwards arrow on top equals negative 2 i with hat on top minus 6 j with hat on top.

a) menentukan vektor a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top

table attributes columnalign right center left columnspacing 2px end attributes row cell a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell open parentheses 5 i with hat on top minus 12 j with hat on top close parentheses minus 2 open parentheses 3 i with hat on top minus 4 j with hat on top close parentheses minus open parentheses negative 2 i with hat on top minus 6 j with hat on top close parentheses end cell row blank equals cell 5 i with hat on top minus 12 j with hat on top minus 6 i with hat on top plus 8 j with hat on top plus 2 i with hat on top plus 6 j with hat on top end cell row cell a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top end cell equals cell i with hat on top plus 2 j with hat on top end cell end table

b) menentukan vektor 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top

table attributes columnalign right center left columnspacing 2px end attributes row cell 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top end cell equals cell 2 open parentheses 5 i with hat on top minus 12 j with hat on top close parentheses plus open parentheses 3 i with hat on top minus 4 j with hat on top close parentheses minus 1 half open parentheses negative 2 i with hat on top minus 6 j with hat on top close parentheses end cell row blank equals cell 10 i with hat on top minus 24 j with hat on top plus 3 i with hat on top minus 4 j with hat on top plus i with hat on top plus 3 j with hat on top end cell row cell 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top end cell equals cell 14 i with hat on top minus 25 j with hat on top end cell end table

Jadi, diperoleh a with rightwards arrow on top minus 2 b with rightwards arrow on top minus c with rightwards arrow on top equals i with hat on top plus 2 j with hat on top dan 2 a with rightwards arrow on top plus b with rightwards arrow on top minus 1 half c with rightwards arrow on top equals 14 i with hat on top minus 25 j with hat on top.

Perdalam pemahamanmu bersama Master Teacher
di sesi Live Teaching, GRATIS!

30

Iklan

Iklan

Pertanyaan serupa

Diketahui koordinat A ( − 1 , 2 , 3 ) , B ( 4 , − 5 , 0 ) , dan C ( − 2 , − 1 , 3 ) . Jika a , b , dan c merupakan vektor posisi dari A , B , dan C , tentukan : d. cosinus sudut antara vektor ( 2 a...

20

0.0

Jawaban terverifikasi

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Roboguru

Coba GRATIS Aplikasi Ruangguru

Download di Google PlayDownload di AppstoreDownload di App Gallery

Produk Ruangguru

Hubungi Kami

Ruangguru WhatsApp

+62 815-7441-0000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2024 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia