Pertanyaan

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

Diketahui vektor-vektor:

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

Tentukan vektor satuan dari $a, b, c, dan d$ !

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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 straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top comma space dan space straight d with rightwards arrow on top :

Jadi, vektor satuan straight a with rightwards arrow on top comma space straight b with rightwards arrow on top comma space straight c with rightwards arrow on top comma space dan space straight d with rightwards arrow on top :

$table attributes columnalign right center left columnspacing 0px end attributes row cell vektor space satuan space straight a with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar straight a close vertical bar end fraction times space straight a with rightwards arrow on top end cell row blank equals cell 1 over 6 open parentheses table row 6 row 0 end table close parentheses end cell row blank equals cell open parentheses table row 1 row 0 end table close parentheses end cell row cell vektor space satuan space straight b with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar straight b close vertical bar end fraction times space straight b with rightwards arrow on top end cell row blank equals cell 1 fifth open parentheses table row cell negative 3 end cell row cell negative 4 end cell 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 end cell row cell vektor space satuan space straight c with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar straight c close vertical bar end fraction times space straight c with rightwards arrow on top end cell row blank equals cell fraction numerator 1 over denominator square root of 29 end fraction open parentheses table row 5 row 2 end table close parentheses end cell row blank equals cell open parentheses table row cell fraction numerator 5 over denominator square root of 29 end fraction end cell row cell fraction numerator 2 over denominator square root of 29 end fraction end cell end table close parentheses end cell row cell vektor space satuan space straight d with rightwards arrow on top end cell equals cell fraction numerator 1 over denominator open vertical bar straight d close vertical bar end fraction times space straight d with rightwards arrow on top end cell row blank equals cell fraction numerator 1 over denominator square root of 17 end fraction 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 fraction numerator 4 over denominator square root of 17 end fraction end cell row cell fraction numerator negative 1 over denominator square root of 17 end fraction end cell end table close parentheses end cell end table$