Iklan

Iklan

Pertanyaan

Diketahui vektor a = ( − 3 4 ​ ) , b = ( 2 3 ​ ) , dan c = ( − 1 2 ​ ) b. Tentukan vektor sauan dari vektor a , vektor b dan vektor c

Diketahui vektor , , dan

b. Tentukan vektor sauan dari vektor , vektor  dan vektor

Iklan

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Iklan

Pembahasan

Untuk menyelesaikan soal di atas dapat kita selesaikan dengan menggunakan rumus: Pertama kita menentukan panjang dari masing-masing vektor di atas: Maka vektor satuannya adalah:

Untuk menyelesaikan soal di atas dapat kita selesaikan dengan menggunakan rumus:

begin mathsize 14px style a equals fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction end style 

Pertama kita menentukan panjang dari masing-masing vektor di atas:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell vertical line a with rightwards arrow on top vertical line end cell end table equals square root of open parentheses a subscript 1 close parentheses squared plus open parentheses a subscript 2 close parentheses squared plus open parentheses a subscript 3 close parentheses squared plus... plus open parentheses a subscript n close parentheses squared end root comma space maka end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line straight a with rightwards arrow on top vertical line end cell equals cell square root of open parentheses negative 3 close parentheses squared plus open parentheses 4 close parentheses squared end root end cell row cell vertical line straight a with rightwards arrow on top vertical line end cell equals cell square root of 9 plus 16 end root end cell row cell vertical line straight a with rightwards arrow on top vertical line end cell equals cell square root of 25 end cell row cell vertical line straight a with rightwards arrow on top vertical line end cell equals 5 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line b with rightwards arrow on top vertical line end cell equals cell square root of open parentheses 2 close parentheses squared plus open parentheses 3 close parentheses squared end root end cell row cell vertical line b with rightwards arrow on top vertical line end cell equals cell square root of 4 plus 9 end root end cell row cell vertical line b with rightwards arrow on top vertical line end cell equals cell square root of 13 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell vertical line c with rightwards arrow on top vertical line end cell equals cell square root of left parenthesis negative 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end cell row cell vertical line c with rightwards arrow on top vertical line end cell equals cell square root of 5 end cell end table end style

Maka vektor satuannya adalah:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row a equals cell fraction numerator a with rightwards arrow on top over denominator open vertical bar a with rightwards arrow on top close vertical bar end fraction end cell row a equals cell fraction numerator open parentheses table row cell negative 3 end cell row 4 end table close parentheses over denominator 5 end fraction end cell row a equals cell 1 fifth open parentheses table row cell negative 3 end cell row 4 end table close parentheses end cell row a equals cell open parentheses table row cell bevelled fraction numerator negative 3 over denominator 5 end fraction end cell row cell bevelled 4 over 5 end cell end table close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row b equals cell fraction numerator b with rightwards arrow on top over denominator open vertical bar b with rightwards arrow on top close vertical bar end fraction end cell row b equals cell fraction numerator open parentheses table row 2 row 3 end table close parentheses over denominator square root of 13 end fraction end cell row b equals cell fraction numerator 1 over denominator square root of 13 end fraction open parentheses table row 2 row 3 end table close parentheses end cell row b equals cell open parentheses table row cell bevelled fraction numerator 2 over denominator square root of 13 end fraction end cell row cell bevelled fraction numerator 3 over denominator square root of 13 end fraction end cell end table close parentheses end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row c equals cell fraction numerator c with rightwards arrow on top over denominator vertical line c with rightwards arrow on top vertical line end fraction end cell row b equals cell fraction numerator blank over denominator square root of 5 end fraction end cell row b equals cell fraction numerator 1 over denominator square root of 5 end fraction open parentheses table row cell negative 1 end cell row 2 end table close parentheses end cell row b equals cell open parentheses table row cell bevelled fraction numerator negative 1 over denominator square root of 5 end fraction end cell row cell bevelled fraction numerator 2 over denominator square root of 5 end fraction end cell end table close parentheses end cell end table end style

 

221

Iklan

Iklan

Pertanyaan serupa

Misalkan P = 8 i + 15 j ​ . a. Carilah ∣ ∣ ​ P ∣ ∣ ​ b. Tunjukkan bahwa ∣ ∣ ​ P ∣ ∣ ​ P ​ adalah vektor satuan.

2rb+

4.6

Jawaban terverifikasi

Iklan

Iklan

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

Fitur Roboguru

Topik Roboguru

Hubungi Kami

Ruangguru WhatsApp

081578200000

Email info@ruangguru.com

info@ruangguru.com

Contact 02140008000

02140008000

Ikuti Kami

©2022 Ruangguru. All Rights Reserved PT. Ruang Raya Indonesia