Roboguru

Diketahui vektor , , dan b. Tentukan vektor sauan dari vektor , vektor  dan vektor

Pertanyaan

Diketahui vektor begin mathsize 14px style a with rightwards arrow on top equals open parentheses table row cell negative 3 end cell row 4 end table close parentheses end style, begin mathsize 14px style b with rightwards arrow on top equals open parentheses table row 2 row 3 end table close parentheses end style, dan begin mathsize 14px style c with rightwards arrow on top equals open parentheses table row cell negative 1 end cell row 2 end table close parentheses end style

b. Tentukan vektor sauan dari vektor begin mathsize 14px style a with rightwards arrow on top end style, vektor  begin mathsize 14px style b with rightwards arrow on top end style dan vektor begin mathsize 14px style c with rightwards arrow on top end style

Pembahasan Soal:

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

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

RUANGGURU HQ

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

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved