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 $a = (- 3 4)$ , $b = (23)$ , dan $c = (- 1 2)$

b. Tentukan vektor sauan dari vektor $a$ , vektor $b$ dan vektor $c$

M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

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:

Maka vektor satuannya adalah:

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

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

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