a=7i+5j​−3k b=5i+2j​+3k, dan c=a−b. Tentukan vektor satuan yang berlawanan dengan c adalah ....

Pertanyaan

begin mathsize 14px style a with rightwards arrow on top equals 7 i with rightwards arrow on top plus 5 j with rightwards arrow on top minus 3 k with rightwards arrow on top end style
begin mathsize 14px style b with rightwards arrow on top equals 5 i with rightwards arrow on top plus 2 j with rightwards arrow on top plus 3 k with rightwards arrow on top end style, dan
begin mathsize 14px style c with rightwards arrow on top equals a with rightwards arrow on top minus b with rightwards arrow on top end style.

Tentukan vektor satuan yang berlawanan dengan begin mathsize 14px style c with rightwards arrow on top end style adalah ....

  1. begin mathsize 14px style horizontal ellipsis end style 

  2. begin mathsize 14px style horizontal ellipsis end style 

I. Kumaralalita

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

 vektor satuan yang berlawanan dengan begin mathsize 14px style c with rightwards arrow on top end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative fraction numerator 2 over denominator square root of 19 end fraction end cell row cell negative fraction numerator 3 over denominator square root of 19 end fraction end cell row cell fraction numerator 6 over denominator square root of 19 end fraction end cell end table close parentheses end cell end table end style 

Pembahasan

Diberikan vektor begin mathsize 14px style c with rightwards arrow on top equals a with rightwards arrow on top minus b with rightwards arrow on top end style. Dimisalkan vektor begin mathsize 14px style top enclose p end style adalah vektor yang berlawanan arah dengan vektor begin mathsize 14px style top enclose c end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell top enclose p end cell equals cell negative open parentheses top enclose a minus top enclose b close parentheses end cell row blank equals cell negative open parentheses open parentheses table row 7 row 5 row cell negative 3 end cell end table close parentheses minus open parentheses table row 5 row 2 row 3 end table close parentheses close parentheses end cell row blank equals cell negative open parentheses table attributes columnalign center end attributes row 2 row cell 3 minus 6 end cell end table close parentheses end cell row blank equals cell open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses end cell end table end style 

Vektor satuan dari vektor begin mathsize 14px style top enclose p end style adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell p with hat on top end cell equals cell fraction numerator top enclose p over denominator open vertical bar top enclose p close vertical bar end fraction end cell row blank equals cell fraction numerator open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses over denominator square root of left parenthesis negative 2 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared plus 6 end root end fraction end cell row blank equals cell fraction numerator 1 over denominator square root of 4 plus 9 plus 6 end root end fraction times open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses end cell row blank equals cell fraction numerator 1 over denominator square root of 19 end fraction times open parentheses table row cell negative 2 end cell row cell negative 3 end cell row 6 end table close parentheses end cell row blank equals cell open parentheses table row cell negative fraction numerator 2 over denominator square root of 19 end fraction end cell row cell negative fraction numerator 3 over denominator square root of 19 end fraction end cell row cell fraction numerator 6 over denominator square root of 19 end fraction end cell end table close parentheses end cell end table end style  

Jadi, vektor satuan yang berlawanan dengan begin mathsize 14px style c with rightwards arrow on top end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses table row cell negative fraction numerator 2 over denominator square root of 19 end fraction end cell row cell negative fraction numerator 3 over denominator square root of 19 end fraction end cell row cell fraction numerator 6 over denominator square root of 19 end fraction end cell end table close parentheses end cell end table end style 

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Diketahui tiga buah vektor sebagai berikut. uvw​===​2i⌢+2j⌢​−k⌢2i⌢−j⌢​+3k⌢i⌢+j⌢​−k⌢​ Tentukanlah: a. Vektor satuan dari u⌢

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