Pertanyaan

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

Diketahui vektor-vektor:

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

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

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 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top :

$table attributes columnalign right center left columnspacing 0px end attributes row cell 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top end cell equals cell 1 third open parentheses table row cell negative 3 end cell row cell negative 4 end cell end table close parentheses minus 2 open parentheses table row 5 row 2 end table close parentheses plus 5 open parentheses table row 4 row cell negative 1 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 1 end cell row cell fraction numerator negative 4 over denominator 3 end fraction end cell end table close parentheses minus open parentheses table row 10 row 4 end table close parentheses plus open parentheses table row 20 row cell negative 5 end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 row cell fraction numerator negative 4 minus 12 minus 15 over denominator 3 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row 9 row cell fraction numerator negative 31 over denominator 3 end fraction end cell end table close parentheses end cell row cell open vertical bar 1 third straight b minus 2 straight c plus 5 straight d close vertical bar end cell equals cell square root of 9 squared plus open parentheses fraction numerator negative 31 over denominator 3 end fraction close parentheses squared end root end cell row blank equals cell square root of 81 plus 961 over 9 end root end cell row blank equals cell square root of fraction numerator 243 plus 961 over denominator 9 end fraction end root end cell row blank equals cell square root of fraction numerator 1.204 over denominator 9 end fraction end root end cell row blank equals cell 2 square root of 301 over 9 end root end cell row blank equals cell 2 over 3 square root of 301 end cell end table$

Jadi, vektor satuan 2 straight a with rightwards arrow on top minus straight c with rightwards arrow on top minus straight d with rightwards arrow on top :

$table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar begin display style 1 third straight b minus 2 straight c plus 5 straight d end style close vertical bar end fraction times open parentheses 1 third straight b with rightwards arrow on top minus 2 straight c with rightwards arrow on top plus 5 straight d with rightwards arrow on top close parentheses end cell row blank equals cell fraction numerator 1 over denominator 2 over 3 square root of 301 end fraction open parentheses table row 9 row cell fraction numerator negative 31 over denominator 3 end fraction end cell end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 27 over denominator 2 square root of 301 end fraction end cell row cell fraction numerator negative 93 over denominator 6 square root of 301 end fraction end cell end table close parentheses end cell end table$