Pertanyaan

Diketahui vektor-vektor: a = ( 6 0 ) , b = ( − 3 − 4 ) , c = ( 5 2 ) , dan d = ( 4 − 1 ) Tentukan vektor satuan dari 5 1 b − 3 2 c − 7 a !

Diketahui vektor-vektor:

$a = (60), b = (- 3 - 4), c = (52), dan d = (4 - 1)$

Tentukan vektor satuan dari $\frac{1}{5} b - \frac{2}{3} c - 7 a$ !

Z. Apriani

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

Jawaban terverifikasi

Pembahasan

Ingat bahwa vektor satuan adalah vektor yang panjangnya sama dengan satu. Berdasarkan soal diketahui , sehingga panjang vektor : Jadi,vektor satuan :

Ingat bahwa vektor satuan adalah vektor yang panjangnya sama dengan satu. Berdasarkan soal diketahui , sehingga panjang vektor 1 fifth straight b with rightwards arrow on top minus 2 over 3 straight c with rightwards arrow on top minus 7 straight a with rightwards arrow on top :

$table attributes columnalign right center left columnspacing 0px end attributes row cell 1 fifth straight b with rightwards arrow on top minus 2 over 3 straight c with rightwards arrow on top minus 7 straight a with rightwards arrow on top end cell equals cell 1 fifth open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses minus 2 over 3 open parentheses table row 5 row 2 end table close parentheses minus 7 open parentheses table row 6 row 0 end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator negative 3 over denominator 5 end fraction end cell row cell fraction numerator negative 4 over denominator 5 end fraction end cell end table close parentheses minus open parentheses table row cell 10 over 3 end cell row cell 4 over 3 end cell end table close parentheses minus open parentheses table row 42 row 0 end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator negative 9 minus 50 minus 630 over denominator 15 end fraction end cell row cell fraction numerator negative 12 minus 20 over denominator 15 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 45 comma 93 end cell row cell 2 comma 13 end cell end table close parentheses end cell row cell open vertical bar 1 fifth straight b minus 2 over 3 straight c minus 7 straight a close vertical bar end cell equals cell square root of 45 comma 93 squared plus 2 comma 13 squared end root end cell row blank equals cell 45 comma 98 end cell end table$

Jadi, vektor satuan 1 fifth straight b with rightwards arrow on top minus 2 over 3 straight c with rightwards arrow on top minus 7 straight a with rightwards arrow on top :

$table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space 1 fifth straight b with rightwards arrow on top minus 2 over 3 straight c with rightwards arrow on top minus 7 straight a with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar begin display style 1 fifth straight b minus fraction numerator begin display style 2 end style over denominator 3 end fraction straight c minus 7 straight a end style close vertical bar end fraction times open parentheses 1 fifth straight b with rightwards arrow on top minus 2 over 3 straight c with rightwards arrow on top minus 7 straight a with rightwards arrow on top close parentheses end cell row blank equals cell fraction numerator 1 over denominator 45 comma 98 end fraction open parentheses table row cell 45 comma 93 end cell row cell 2 comma 13 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell 2 comma 111 end cell row cell 0 comma 046 end cell end table close parentheses end cell end table$